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

a noisy principal component analysis for forward rate curves abstract principal component analysis pca is the most common nonparametric method for estimating the volatility structure of gaussian interest rate models one major difficulty in the estimation of these models is the fact that forward rate curves are not directly observable from the market so that non trivial observational errors arise in any statistical analysis in this work we point out that the classical pca analysis is not suitable for estimating factors of forward rate curves due to the presence of measurement errors induced by market microstructure effects and numerical interpolation our analysis indicates that the pca based on the long run covariance matrix is capable to extract the true covariance structure of the forward rate curves in the presence of observational errors moreover it provides a significant reduction in the pricing errors due to noisy data typically found in forward rate curves

clustering of trend data using joinpoint regression models in this paper we propose methods to cluster groups of two dimensional data whose mean functions are piecewise linear into several clusters with common characteristics such as the same slopes to fit segmented line regression models with common features for each possible cluster we use a restricted least squares method in implementing the restricted least squares method we estimate the maximum number of segments in each cluster by using both the permutation test method and the bayes information criterion method and then propose to use the bayes information criterion to determine the number of clusters for a more effective implementation of the clustering algorithm we propose a measure of the minimum distance worth detecting and illustrate its use in two examples we summarize simulation results to study properties of the proposed methods and also prove the consistency of the cluster grouping estimated with a given number of clusters the presentation and examples in this paper focus on the segmented line regression model with the ordered values of the independent variable which has been the model of interest in cancer trend analysis but the proposed method can be applied to a general model with design points either ordered or unordered copyright 2014 john wiley sons ltd

on the ramanujan conjecture over number fields we extend to an arbitrary number eld the best known bounds towards ramanujan for the group gln n 2 3 4 in particular we present a technique which overcomes the analytic obstacles posed by the presence of an innite group of units

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

fixed smoothing asymptotics in a two step generalized method of moments framework fixed smoothing asymptotics this paper develops the fixed smoothing asymptotics in a two step generalized method of moments gmm framework under this type of asymptotics the weighting matrix in the second step gmm criterion function converges weakly to a random matrix and the two step gmm estimator is asymptotically mixed normal nevertheless the wald statistic the gmm criterion function statistic and the lagrange multiplier statistic remain asymptotically pivotal it is shown that critical values from the fixed smoothing asymptotic distribution are high order correct under the conventional increasing smoothing asymptotics when an orthonormal series covariance estimator is used the critical values can be approximated very well by the quantiles of a noncentral f distribution a simulation study shows that statistical tests based on the new fixed smoothing approximation are much more accurate in size than existing tests

on a certain metaplectic eisenstein series and the twisted symmetric square l function in our earlier paper based on a paper by bump and ginzburg we used an eisenstein series on the double cover of text gl r to obtain an integral representation of the twisted symmetric square l function of text gl r using that we showed that the incomplete twisted symmetric square l function of text gl r is holomorphic for text re s 1 in this paper we will determine the possible poles of this eisenstein series more precisely and show that the incomplete twisted symmetric square l function is entire except possible simple poles at s 0 and s 1

the twisted symmetric square l function of gl r in this paper we consider the partial symmetric square l function ls s sym2 of an irreducible cuspidal automorphic representation of glr a twisted by a hecke character in particular we will show that the l function ls s sym2 is holomorphic for the region re s 1 1 r with the exception that if r 2 1 a pole might occur at s 1 where is the central character of our method of proof is essentially a nontrivial modification of the one by bump and ginzburg in which they considered the case 1

twisted symmetric square l functions for mathrm gl _n and invariant trilinear forms following the works of bump and ginzburg and of takeda we develop a theory of twisted symmetric square l functions for mathrm gl n we characterize their pole in terms of certain trilinear period integrals determine all irreducible summands of the discrete spectrum of mathrm gl n having nonvanishing trilinear periods and construct nonzero local invariant trilinear forms on a certain family of induced representations

eigenvalue ratio test for the number of factors this paper proposes two new estimators for determining the number of factors r in static approximate factor models we exploit the well known fact that the r largest eigenvalues of the variance matrix of n response variables grow unboundedly as n increases while the other eigenvalues remain bounded the new estimators are obtained simply by maximizing the ratio of two adjacent eigenvalues our simulation results provide promising evidence for the two estimators

approximating term structure of interest rates using cubic l1 splines abstract classical spline fitting methods for estimating the term structure of interest rates have been criticized for generating highly fluctuating fitting curves for bond price and discount function in addition the performance of these methods usually relies heavily on parameter tuning involving human judgement to overcome these drawbacks a recently developed cubic l 1 spline model is proposed for term structure analysis cubic l 1 splines preserve the shape of the data exhibit no extraneous oscillation and have small fitting errors cubic l 1 splines are tested using a set of real financial data and compared with the widely used b splines

heteroskedasticity autocorrelation robust standard errors using the bartlett kernel without truncation in this paper we analyze heteroskedasticity autocorrelation hac robust tests constructed using the bartlett kernel without truncation we show that while such an hac estimator is not consistent asymptotically valid testing is still possible we show that tests using the bartlett kernel without truncation are exactly equivalent to recent hac robust tests proposed by kiefer vogelsang and bunzel 2000 econometrica 68 pp 695 714

rationality and holomorphy of langlands shahidi l functions over function fields we prove that all langlands shahidi automorphic l functions over function fields are rational after twists by highly ramified characters they become polynomials and if pi is a globally generic cuspidal automorphic representation of a split classical group or a unitary group and tau is a cuspidal unitary automorphic representation of a general linear group then l s pi times tau is holomorphic for mathfrak r s 1 and has at most a simple pole at s 1 we also prove the holomorphy and non vanishing of automorphic exterior square symmetric square and asai l functions for mathfrak r s 1 finally we complete previous results on functoriality for the classical groups over function fields with applications to the ramanujan conjecture and riemann hypothesis

a proof of langland s conjecture on plancherel measures complementary series of p adic groups analysis of p adic reductive groups our first result theorem 7 9 proves a conjecture of langlands on normalization of intertwining operators by means of local langlands root numbers and l functions at least when the group is quasi split and the inducing representation is generic assuming two natural conjectures in harmonic analysis of p adic groups we also prove the validity of the conjecture in general theorem 9 5 as our second result we obtain all the complementary series and special representations of quasi split p adic groups coming from rank one parabolic subgroups and generic supercuspidal represen

doubling constructions and tensor product l functions the linear case we present an integral representation for the tensor product l function of a pair of automorphic cuspidal representations one of a classical group the other of a general linear group our construction is uniform over all classical groups and is applicable to all cuspidal representations it does not require genericity the main new ideas of the construction are the use of generalized speh representations as inducing data for the eisenstein series and the introduction of a new global and local model which generalizes the whittaker model here we consider linear groups but our construction also extends to arbitrary degree metaplectic coverings this will be the topic of an upcoming work

block compatible metaplectic cocycles has cardinality r 1 let g be the f rational points of a simple chevalley group defined over f in his thesis matsumoto 5 gave a beautiful construction for the metaplectic cover g of g a central extension of g by r f whose existence is intimately connected with the deep properties of the r th order hilbert symbol f f f r f metaplectic groups figure prominently in the study of number theory representation theory and physics arising naturally in the theory of theta functions dual pair correspondences weil representations and spin geometry in this paper we study the class of central extensions of a simple chevalley group over an arbitrary infinite field of which the metaplectic groups form an important subclass metaplectic groups were constructed quite explicitly in weil s memoir 10 in the case that g is symplectic in 3 and 4 kubota gave the construction of the r fold metaplectic cover of gl2 f moreover he described an explicit 2 cocycle k on gl2 f that represents the second cohomology class of the extension cf 3 corollary 8 which makes it possible to deal quite rapidly with many concrete problems in this setting steinberg 9 and moore 7 considered the algebraic problem of determining the central extensions of a simple chevelley group over an arbitrary field they were also led to the metaplectic groups this line of investigation was completed by matsumoto 5 whose work forms the foundation of the present paper to summarize our results let f be an infinite field g the f rational points of a simple chevalley group defined over f a an abelian group and c f f a a steinberg symbol that is bilinear if g is not symplectic cf 1 in this paper we describe an explicit 2 cocycle g in z g a that represents the cohomology class in h g a of the central extension g of g by a constructed by matsumoto 5

theta distinguished representations inflation and the symmetric square l function a theta distinguished representation is a quotient of a tensor of exceptional representations where exceptional is in the sense of kazhdan and patterson we study relations between theta distinguished representations of mathrm gl n and mathrm gspin 2n 1 in the case of mathrm gspin 2n 1 or mathrm so 2n 1 exceptional or small representations were constructed by bump friedberg and ginzburg we prove a rodier type hereditary property a tempered representation tau is distinguished if and only if the representation mathrm i tau induced to mathrm gspin 2n 1 is distinguished and the multiplicity of both quotients is at most one if tau is supercuspidal and distinguished then so is the langlands quotient of mathrm i tau as a corollary we characterize supercuspidal distinguished representations in terms of the pole of the symmetric square l function at s 0