selberg s orthogonality conjecture for automorphic l functions let and be automorphic irreducible unitary cuspidal representations of inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i and inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i respectively assume that either or is self contragredient under the ramanujan conjecture on and we deduce a prime number theorem for l s inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 03i which can be used to asymptotically describe whether or det i 0 for some nonzero 0 inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 04i or det it for any t inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 05i as a consequence we prove the selberg orthogonality conjecture in a more precise form for automorphic l functions l s and l s under the ramanujan conjecture when m m 2 and and are representations corresponding to holomorphic cusp forms our results are unconditional

generalized whittaker models and the bernstein center let f be a non archimedean local field and g the group of f points of a connected reductive algebraic group defined over f let b be a minimal f parabolic subgroup of g with levi component t and unipotent radical u we let be a smooth character of u nondegenerate in a certain sense we consider the theory of smooth whittaker functions on g via the structure of the representation c ind of g which is compactly induced by we prove a finiteness result for these generalized whittaker models corresponding to the uniqueness property for classical whittaker models on quasi split groups in many cases including the one where g is quasi split we describe the ring of g endomorphisms of c ind in terms of the bernstein center this has consequences for the structure of the category of smooth representations of g it gives an algebraic technique for finding improved and more general versions of results on classical whittaker functions originally obtained by more analytic methods

une preuve simple des conjectures de langlands pour gl n sur un corps p adique let f be a finite extension of p for each integer n 1 we construct a bijection from the set f 0 n of isomorphism classes of irreducible degree n representations of the absolute weil group of f onto the set f 0 n of isomorphism classes of smooth irreducible supercuspidal representations of gl n f those bijections preserve epsilon factors for pairs and hence we obtain a proof of the langlands conjectures for gl n over f which is more direct than harris and taylor s our approach is global and analogous to the derivation of local class field theory from global class field theory we start with a result of kottwitz and clozel on the good reduction of some shimura varieties and we use a trick of harris who constructs non galois automorphic induction in certain cases

minimum leaf out branching and related problems given a digraph d the minimum leaf out branching problem minlob is the problem of finding in d an out branching with the minimum possible number of leaves i e vertices of out degree 0 we prove that minlob is polynomial time solvable for acyclic digraphs in general minlob is np hard and we consider three parameterizations of minlob we prove that two of them are np complete for every value of the parameter but the third one is fixed parameter tractable fpt the fpt parameterization is as follows given a digraph d of order n and a positive integral parameter k check whether d contains an out branching with at most n k leaves and find such an out branching if it exists we find a problem kernel of order o k 2 and construct an algorithm of running time o 2 o k l o g k n 6 which is an additive fpt algorithm we also consider transformations from two related problems the minimum path covering and the maximum internal out tree problems into minlob which imply that some parameterizations of the two problems are fpt as well

on existence of generic cusp forms on semisimple algebraic groups in this paper we discuss the existence of certain classes of cuspidal automorphic representations having non zero fourier coefficients for a general semisimple algebraic group g defined over a number field k such that its archimedean group g infty is not compact when g is quasi split over k we obtain a result on existence of generic cuspidal automorphic representations which generalize results of vigneras henniart and shahidi we also discuss i the existence of cuspidal automorphic forms with non zero fourier coefficients for congruence of subgroups of g infty and ii applications related to the work of bushnell and henniart on generalized whittaker models

on the ramanujan conjecture and finiteness of poles for certain l functions in this paper we prove a number of general results about automorphic l functions which appear in the constant terms of eisenstein series for an arbitrary quasi split connected reductive algebraic group over a number field these l functions were first introduced by langlands for chevalley groups 20 and through them he was led to make some of his deep conjectures 21 one significance of these l functions is that all the automorphic l functions studied so far are among them there are three general results first we obtain a uniform line of absolute convergence for all of these l functions theorem 5 1 a uniform estimate for the hecke eigenvalues of generic cusp forms on many absolutely simple quasi split connected reductive algebraic groups over number fields corollary 5 4 and an improvement on the best available estimate for the fourier coefficients of maass wave forms corollary 5 5 also follow next we establish a meromorphic continuation and functional equation for each of these l functions theorem 6 1 finally in theorem 6 2 we prove finiteness of poles on the whole complex plane for an important class of these l functions corollaries 6 6 through 6 10 more precisely let g be a quasi split connected reductive algebraic group over a number field f set g g a f where a f is the ring of adeles of f fix a borel subgroup b of g over f and let u be its unipotent radical let p be a maximal f parabolic subgroup of g with p d b in the context of the problems studied here nothing new will be obtained if one drops the maximality condition on p write p mn a levi decomposition n c u and let b u p m and n be the corresponding groups of adelic points for every place v of f let gv g fj similarly we have bv us pv me and nv let x xv be a generic character of u f u cf section 3 then each xv is generic let r ov 7tv be a cusp form on m we shall say 7t is

a matter of degree improved approximation algorithms for degree bounded minimum spanning trees in this paper we present a new bicriteria approximation algorithm for the degree bounded minimum spanning tree problem in this problem we are given an undirected graph a nonnegative cost function on the edges and a positive integer b and the goal is to find a minimum cost spanning tree t with maximum degree at most b in an n node graph our algorithm finds a spanning tree with maximum degree o b logn and cost o optb where optb is the minimum cost of any spanning tree whose maximum degree is at most b our algorithm uses ideas from lagrangean duality we show how a set of optimum lagrangean multipliers yields bounds on both the degree and the cost of the computed solution

on the generic local langlands correspondence for gspin groups in the case of split gspin groups we prove an equality of l functions between automorphic local l functions defined by the langlands shahidi method and local artin l functions our method of proof is based on previous results of the first author which allow to reduce the problem to supercuspidal representations of levi subgroups of gspin by constructing langlands parameters for general generic irreducible admissible representations of gspin from the one for generic irreducible supercuspidal representations of its levi subgroups

primal dual meets local search approximating msts with nonuniform degree bounds we present a new bicriteria approximation algorithm for the degree bounded minimum cost spanning tree mst problem given an undirected graph with nonnegative edge weights and a degree bound b find a spanning tree of maximum node degree b and minimum total edge cost our algorithm outputs a tree of maximum degree at most a constant times b and total edge cost at most a constant times that of a minimum cost degree b bounded spanning tree while our new algorithm is based on ideas from lagrangian relaxation as is our previous work siam j comput 31 2002 pp 1783 1793 it does not rely on computing a solution to a linear program instead it uses a repeated application of kruskal s mst algorithm interleaved with a combinatorial update of approximate lagrangian node multipliers maintained by the algorithm these updates cause subsequent repetitions of the spanning tree algorithm to run for longer and longer times leading to overall progress and a proof of the performance guarantee a second useful feature of our algorithm is that it can handle nonuniform degree bounds on the nodes given distinct bounds bv for every node v in v the output tree has degree at most o bv log v for every v in v as before the cost of the tree is at most a constant times that of a minimum cost tree obeying all degree bounds

test vectors for finite periods and base change abstract let e f be a quadratic extension of finite fields by a result of gow an irreducible representation of g gl n e has at most one non zero h invariant vector up to multiplication by scalars when h is gl n f or u n e f if does have an h invariant vector it is said to be h distinguished it is known from the work of gow that h distinction is characterized by base change from u n e f due to kawanaka when h is gl n f resp from gl n f due to shintani when h is u n e f assuming is generic and h distinguished we give an explicit description of the h invariant vector in terms of the bessel function of let be a non degenerate character of n g n h and let b be the normalized bessel function of on the whittaker model for the h average w 1 h h h h b of the bessel function we prove that w i n dim dim gl n e gl n f u n e f where is the irreducible representation of u n e f resp gl n f that base changes to when h is gl n f resp u n e f as an application we classify the members of a generic l packet of sl n e that admit invariant vectors for sl n f finally we prove a p adic analogue of our result for square integrable representations in terms of formal degrees by employing the formal degree conjecture of hiraga ichino ikeda 19

quasinormability and topologies on spaces of polynomials abstract an example of a frechet spaceeis given such that the space ofn homogeneous continuous polynomials one endowed with any of the natural topologies usually considered on it is quasinormable for everyn n this space has the particularity that all the natural topologies are different on it forn 2

deeper local search for parameterized and approximation algorithms for maximum internal spanning tree the maximum internal spanning tree problem asks for a spanning tree of a given graph that has the maximum number of internal vertices among all spanning trees of this graph in its parameterized version we are interested in whether the graph has a spanning tree with at least k internal vertices fomin et al 2013 4 crafted a very ingenious reduction rule and showed that a simple application of this rule is sufficient to yield a 3k vertex kernel implying an o 8 k time parameterized algorithm using depth 2 local search knauer and spoerhase 2015 9 developed a 5 3 approximation algorithm for the optimization version we try deeper local search we conduct a thorough combinatorial analysis on the obtained spanning trees and explore their algorithmic consequences we first observe that from the spanning tree obtained by depth 3 local search one can easily find a reducible structure and apply the reduction rule of fomin et al this gives an improved kernel of 2k vertices and as a by product a deterministic algorithm running in time o 4 k we then go even deeper by considering the spanning tree obtained by depth 5 local search it is shown that the number of internal vertices of this spanning tree is at least 2 3 of the maximum number a spanning tree can have thereby delivering an improved approximation algorithm with ratio 1 5 for the problem

dealing with several parameterized problems by random methods abstract in this paper we apply random methods to deal with several parameterized problems for the parameterized weighted p 3 packing problem by randomly partitioning the vertices in given graph a tripartite graph can be obtained we prove that the parameterized weighted p 3 packing problem can be solved in polynomial time on tripartite graphs based on the algorithm on tripartite graphs a randomized parameterized algorithm of running time o 32 k is given for the parameterized weighted p 3 packing problem for the parameterized weighted load coloring problem by randomly partitioning the vertices in given graph into two parts and studying the structure properties of the connected components in two parts a randomized parameterized algorithm of running time o 11 32 k is presented for the parameterized claw free edge deletion problem on diamond free graphs by combining random with branching methods a parameterized algorithm of running time o 2 42 k is given

the local langlands correspondence for gsp 4 over local function fields we prove the local langlands correspondence for rm gsp 4 f where f is a non archimedean local field of positive characteristic with residue characteristic 2

local coefficients as artin factors for real groups introduction the purpose of this paper is to prove the equality of certain local coefficients of arithmetic significance which were attached to representations of quasi split real reductive algebraic groups in 27 with their corresponding artin factors attached by local class field theory 21 as a consequence we establish an identity satisfied by certain normalized intertwining operators it seems to be useful in applications of the trace formula 1 29 more precisely let g be the group of real points of a quasi split reductive algebraic group over r let a be the set of simple roots defined by a fixed minimal parabolic subgroup po m0a0u of g fix 6 c a and let p p9 be the corresponding standard parabolic subgroup of g and write p man for its langlands decomposition fix a nondegenerate character x f u i a h o be an irreducible admissible x gic banach in particular x generic unitary representation of m cf section 1 given v g a the complex dual of the lie algebra of a let i v o 0 be the continuously quasi unitarily if o is unitary induced representation indp ga e v 9 and let v v o 0 be its space section 0 then f a vfoo o now let w be the weyl group of ao in g choose w g w such that w 0 c a let n be the unipotent group opposite to n define n u c wn w where w is a representative of w in g for g f a 00 define

on the nonvanishing of the central value of the rankin selberg l functions first published in journal of the american mathematical society in volume 17 issue 3 published by the american mathematical society

parameterized algorithms for edge biclique and related problems abstract maximum edge biclique and related problems have wide applications in management science bioinformatics etc in this paper we study parameterized algorithms for parameterized edge biclique problem parameterized edge biclique packing problem parameterized biclique edge deletion problem and parameterized bipartite biclique clustering problem for the parameterized edge biclique problem the current best result is of running time o 2 k and we give a parameterized algorithm of running time o n k 2 5 k k where k is the parameter and n is the number of vertices in the given graph for the parameterized edge biclique packing problem based on randomized divide and conquer technique a parameterized algorithm of running time o k k l o g k 4 2 k 1 t is given where k is the parameter and t is the number of bicliques in the solution we study the parameterized biclique edge deletion problem on bipartite graphs and general graphs and give parameterized algorithms of running time o 2 k and o 3 k respectively for the parameterized bipartite biclique clustering problem based on modular decomposition method a kernel of size o k 2 and a parameterized algorithm of running time o 2 42 k n m are presented where k is the parameter n is the number of vertices and m is the number of edges in the given graph

local langlands correspondence for mathrm gl _ n and the exterior and symmetric square varepsilon factors let f be a p adic field that is a finite extension of qp for some prime p the local langlands correspondence llc attaches to each continuous n dimensional semisimple representation of w f the weil deligne group for f f an irreducible admissible representation of gln f such that among other things the local l and e factors of pairs are preserved this correspondence should be robust and preserve various parallel operations on the arithmetic and analytic sides such as taking the exterior square or symmetric square in this article we show that this is the case for the local arithmetic and analytic symmetric square and exterior square e factors that is that e s 2 e s 2 and e s sym2 e s sym2 the agreement of the l functions also follows by our methods but this was already known by henniart the proof is a robust deformation argument combined with local global techniques which reduces the problem to the stability of the analytic factor s 2 under highly ramified twists when is supercuspidal this last step is achieved by relating the factor to a mellin transform of a partial bessel function attached to the representation and then analyzing the asymptotics of the partial bessel function inspired in part by the theory of shalika germs for bessel integrals the stability for every irreducible admissible representation then follows from those of the corresponding arithmetic factors as a corollary

generic transfer for general spin groups we prove langlands functoriality for the generic spectrum of general spin groups both odd and even contrary to other recent instances of functoriality our resulting automorphic representations on the general linear group are not self dual together with cases of classical groups this completes the list of cases of split reductive groups whose l groups have classical derived groups the important transfer from gsp4 to gl4 follows from our result as a special case

iwahori component of the gelfand graev representation let g be a split reductive group over a p adic field f let b be a borel subgroup and u the maximal unipotent subgroup of b let psi be a whittaker character of u let i be an iwahori subgroup of g we describe the iwahori hecke algebra action on the gelfand graev representation mathrm ind u g psi i by an explicit hecke algebra module

a projective description of the nachbin ported topology abstract in this article we give a projective description of the nachbin ported topology in h u x the space of holomorphic mappings on a balanced open subsetuof a frechet spacee which satisfies certain general conditions with values in a banach spacexwhich is complemented in its bidual to do this we use the topology bintroduced by dineen math scand 74 1994 215 236 as a consequence we characterize when the compact open topology 0and coincide on h u x for every banach spacex in terms of a condition one among the techniques we use to obtain these results are the bb property the density condition a version of quasinormability and taylor series expansions

local to global extensions for gln in non zero characteristic a characterization of yf s p sym2 v and yf s p a2 v let f be a locally compact field of positive characteristic in his thesis the second author used the langlands shahidi method to define factors for the symmetric square and exterior square representations of the dual group of gl n f we prove here that such factors are characterized by local properties including a multiplicativity property with respect to parabolic induction and their role in global functional equations for l functions for this we prove that a given cuspidal representation of gl n f is the component at some place of a global automorphic representation the ramification of which is controlled at other places in fact we use an equivalent result for l adic galois representations due to o gabber and n katz and transport it via the global langlands correspondence proved by l lafforgue

constant term of smooth h_psi spherical functions on a reductive p adic group let be a smooth character of a closed subgroup h of a reductive p adic group g if p is a parabolic subgroup of g such that ph is open in g we define the constant term of every smooth function on g which transforms by under the right action of g the example of mixed models is given it includes symmetric spaces and whittaker models in this case a notion of cuspidal function is defined and studied it leads to finiteness theorems

a randomized linear time algorithm to find minimum spanning trees we present a randomized linear time algorithm to find a minimum spanning tree in a connected graph with edge weights the algorithm uses random sampling in combination with a recently discovered linear time algorithm for verifying a minimum spanning tree our computational model is a unit cost random access machine with the restriction that the only operations allowed on edge weights are binary comparisons