mazur tate elements of nonordinary modular forms we establish formulae for the iwasawa invariants of mazur tate elements of cuspidal eigenforms generalizing known results in weight 2 our first theorem deals with forms of medium weight and our second deals with forms of small slope we give examples illustrating the strange behavior which can occur in the high weight high slope case

short packet communications over multiple antenna rayleigh fading channels motivated by the current interest in ultra reliable low latency machine type communication systems we investigate the tradeoff between reliability throughput and latency in the transmission of information over multiple antenna rayleigh block fading channels specifically we obtain finite blocklength finite snr upper and lower bounds on the maximum coding rate achievable over such channels for a given constraint on the packet error probability numerical evidence suggests that our bounds delimit tightly the maximum coding rate already for short blocklengths packets of about 100 symbols furthermore our bounds reveal the existence of a tradeoff between the rate gain obtainable by spreading each codeword over all available time frequency spatial degrees of freedom and the rate loss caused by the need of estimating the fading coefficients over these degrees of freedom in particular our bounds allow us to determine the optimal number of transmit antennas and the optimal number of time frequency diversity branches that maximize the rate finally we show that infinite blocklength performance metrics such as the ergodic capacity and the outage capacity yield inaccurate throughput estimates

torsion points on modular curves let n 23 be a prime number in this paper we prove a conjecture of coleman kaskel and ribet about the valued points of the modular curve x 0 n which map to torsion points on j 0 n via the cuspidal embedding we give some generalizations to other modular curves and to noncuspidal embeddings of x 0 n into j 0 n

modularity lifting beyond the taylor wiles method we prove new modularity lifting theorems for p adic galois representations in situations where the methods of wiles and taylor wiles do not apply previous generalizations of these methods have been restricted to situations where the automorphic forms in question contribute to a single degree of cohomology in practice this imposes several restrictions one must be in a shimura variety setting and the automorphic forms must be of regular weight at infinity in this paper we essentially show how to remove these restrictions our most general result is a modularity lifting theorem which on the automorphic side applies to automorphic forms on the group mathrm gl n over a general number field it is contingent on a conjecture which in particular predicts the existence of galois representations associated to torsion classes in the cohomology of the associated locally symmetric space we show that if this conjecture holds then our main theorem implies the following if e is an elliptic curve over an arbitrary number field then e is potentially automorphic and satisfies the sato tate conjecture in addition we also prove some unconditional results for example in the setting of mathrm gl 2 over mathbf q we identify certain minimal global deformation rings with the hecke algebras acting on spaces of p adic katz modular forms of weight 1 such algebras may well contain p torsion moreover we also completely solve the problem for p odd of determining the multiplicity of an irreducible modular representation overline rho in the jacobian j 1 n where n is the minimal level such that overline rho arises in weight two

construction of some families of 2 dimensional crystalline representations we construct explicitly some analytic families of etale modules which give rise to analytic families of 2 dimensional crystalline representations as an application of our constructions we verify some conjectures of breuil on the reduction modulo p of those representations and extend some results of deligne edixhoven fontaine and serre on the representations arising from modular forms

reductions of galois representations of slope 1 abstract we compute the reductions of irreducible crystalline two dimensional representations of g q p of slope 1 for primes p 5 and all weights we describe the semisimplification of the reductions completely in particular we show that the reduction is often reducible we also investigate whether the extension obtained is peu or tres ramifiee in the relevant reducible non semisimple cases the proof uses the compatibility between the p adic and mod p local langlands correspondences and involves a detailed study of the reductions of both the standard and non standard lattices in certain p adic banach spaces

on serre s conjecture for mod l galois representations over totally real fields in 1987 serre conjectured that any mod two dimensional irre ducible odd representation of the absolute galois group of the rationals came from a modular form in a precise way we present a generalisation of this conjecture to 2 dimensional representations of the absolute galois group of a totally real eld where is unramied the hard work is in formulating an analogue of the weight part of serre s conjecture serre furthermore asked whether his conjecture could be rephrased in terms of a mod langlands philosophy using ideas of emerton and vign eras we formulate a mod local global principle for the group d where d is a quaternion algebra over a totally real eld split above and at 0 or 1 innite places and show how it implies the conjecture

on modular representations of bar q q arising from modular forms where g is the galois group gai i q and f is a finite field of characteristic i 3 suppose that p is modular of level n i e that it arises from a weight 2 newform of level dividing n and trivial nebentypus character then p is an odd representation the matrix p c where c is a complex conjugation in g has eigenvalues 1 1 since 1 and 1 are distinct in f p is absolutely irreducible and has a model over every subfield of f containing the set trace p we assume that f has been chosen so that it is generated by this set assume that p is a prime which exactly divides n we write p i n and restrict p to a decomposition group of g for the prime p view the restriction as a representation p p of gal t p qp we say that p is finite at p 34 or 35 w if there is a finite flat f vector space scheme h over zp for which the action of gal t p qp on the f vector space h 1 p gives pp i f p 9 is finite at p if and only if pp is unramified it is clear that p is finite at p whenever p is already modular of level n p in w of 34 cf 35 serre conjectured the converse i e that if p is finite then p is modular of level n p soon thereafter mazur 1 20 proved this conjecture in the case

p adic periods and modular symbols of elliptic curves of prime conductor under certain assumptions we prove a conjecture of mazur and tate describing a relation between the modular symbol attached to an elliptic curve with split multiplicative reduction atp and itsp adic period we generalize this relation to modular forms of weight 2 with coefficients not necessarily in

serre s modularity conjecture ii we provide proofs of theorems 4 1 and 5 1 of khare and wintenberger invent math doi 10 1007 s00222 009 0205 7 2009

weight cycling and serre type conjectures for unitary groups we prove that for forms of u 3 which are compact at infinity and split at places dividing a prime p in generic situations the serre weights of a mod p modular galois representation which is irreducible when restricted to each decomposition group above p are exactly those previously predicted by herzig we do this by combining explicit computations in p adic hodge theory based on a formalism of strongly divisible modules and breuil modules with descent data which we develop here with a technique that we call weight cycling

weights of galois representations associated to hilbert modular forms let f be a totally real field p 3 a rational prime unramified in f and p a place of f over p let gal f f gl2 fp be a two dimensional mod p galois representation which is assumed to be modular of some weight and whose restriction to a decomposition subgroup at p is irreducible we specify a set of weights determined by the restriction of to inertia at p which contains all the modular weights for this proves part of a conjecture of diamond buzzard and jarvis which provides an analogue of serre s epsilon conjecture for hilbert modular forms mod p

langlands base change for gl 2 let f be a totally real galois number eld we prove the existence of base change relative to the extension f q for every holomorphic newform of weight at least 2 and odd level under simple local assumptions on the eld f

on a conjecture of conrad diamond and taylor we prove a conjecture of conrad diamond and taylor on the size of certain deformation rings parametrizing potentially barsotti tate ga lois representations to achieve this we extend results of breuil and m ezard classifying galois lattices in semistable representations in terms of strongly divisible modules to the potentially crystalline case in hodge tate weights 0 1 we then use these strongly divisible modules to compute the desired deformation rings as a corollary we obtain new results on the modularity of potentially barsotti tate representations

l functions of universal elliptic curves over igusa curves this paper is concerned with computing the l functions of the title in terms of modular forms because one can produce zeros of these l functions they seem to provide interesting test cases for various conjectures relating l functions to cycles in the first three sections we state the theorem review some consequences and give a brief sketch of the proof this proof is based on recent results of katz and mazur so in sections 4 through 6 we establish notation by reviewing the relevant parts of their work in sections 7 and 8 we prove an eichler shimura style result on a hecke operator the proof proper occupies sections 9 through 12 the paper 11 provides an introduction to the universal curves over igusa curves

non dissipative space time hp discontinuous galerkin method for the time dependent maxwell equations a finite element method for the solution of the time dependent maxwell equations in mixed form is presented the method allows for local hp refinement in space and in time to this end a space time galerkin approach is employed in contrast to the space time dg method introduced in 1 test and trial spaces do not coincide this allows for obtaining a non dissipative method to obtain an efficient implementation a hierarchical tensor product basis in space and time is proposed this allows to evaluate the local residual with a complexity of o p 4 and o p 5 for affine and non affine elements respectively