scholarly journals Langlands lambda function for quadratic tamely ramified extensions

2019 ◽  
Vol 18 (07) ◽  
pp. 1950132
Author(s):  
Sazzad Ali Biswas
Keyword(s):  
Explicit Formula ◽  
Local Field ◽  
Characteristic Zero

Let [Formula: see text] be a quadratic tamely ramified extension of a non-Archimedean local field [Formula: see text] of characteristic zero. In this paper, we give an explicit formula for Langlands’ lambda function [Formula: see text].

Globalization of Distinguished Supercuspidal Representations of GL(n)

2002 ◽  
Vol 45 (2) ◽  
pp. 220-230 ◽  
Author(s):  
Jeffrey Hakim ◽  
Fiona Murnaghan
Keyword(s):  
Local Field ◽  
Characteristic Zero ◽  
Cuspidal Representation ◽  
Supercuspidal Representation ◽  
Local Component ◽  
Supercuspidal Representations

AbstractAn irreducible supercuspidal representation π of G = GL(n, F), where F is a nonarchimedean local field of characteristic zero, is said to be “distinguished” by a subgroup H of G and a quasicharacter χ of H if HomH(π, χ) ≠ 0. There is a suitable global analogue of this notion for an irreducible, automorphic, cuspidal representation associated to GL(n). Under certain general hypotheses, it is shown in this paper that every distinguished, irreducible, supercuspidal representation may be realized as a local component of a distinguished, irreducible automorphic, cuspidal representation. Applications to the theory of distinguished supercuspidal representations are provided.

scholarly journals The distinction problem for metaplectic case

2020 ◽  
Vol 16 (06) ◽  
pp. 1161-1183
Author(s):  
Hengfei Lu
Keyword(s):  
Local Field ◽  
Characteristic Zero ◽  
Quaternion Algebra ◽  
Quadratic Field ◽  
Field Extension ◽  
Similar Strategy

We use the theta lifts between [Formula: see text] and [Formula: see text] to study the distinction problems for the pair [Formula: see text] where [Formula: see text] is a quadratic field extension over a nonarchimedean local field [Formula: see text] of characteristic zero and [Formula: see text] is a quaternion algebra. With a similar strategy, we give a conjectural formula for the multiplicity of distinction problem related to the pair [Formula: see text]

scholarly journals Twisting of paramodular vectors

2014 ◽  
Vol 10 (04) ◽  
pp. 1043-1065 ◽  
Author(s):  
Jennifer Johnson-Leung ◽  
Brooks Roberts
Keyword(s):  
Local Field ◽  
Characteristic Zero ◽  
Central Character ◽  
Admissible Representation ◽  
Quadratic Character ◽  
Irreducible Admissible Representation

Let F be a non-Archimedean local field of characteristic zero, let (π, V) be an irreducible, admissible representation of GSp (4, F) with trivial central character, and let χ be a quadratic character of F× with conductor c(χ) > 1. We define a twisting operator Tχ from paramodular vectors for π of level n to paramodular vectors for χ ⊗ π of level max (n + 2c(χ), 4c(χ)), and prove that this operator has properties analogous to the well-known GL(2) twisting operator.

scholarly journals LOCAL NEWFORMS AND FORMAL EXTERIOR SQUARE L-FUNCTIONS

2013 ◽  
Vol 09 (08) ◽  
pp. 1995-2010 ◽  
Author(s):  
MICHITAKA MIYAUCHI ◽  
TAKUYA YAMAUCHI
Keyword(s):  
Local Field ◽  
Characteristic Zero ◽  
Principal Series ◽  
Whittaker Function ◽  
Series Representations ◽  
Principal Series Representations ◽  
Exterior Square

Let F be a non-archimedean local field of characteristic zero. Jacquet and Shalika attached a family of zeta integrals to unitary irreducible generic representations π of GL n(F). In this paper, we show that the Jacquet–Shalika integral attains a certain L-function, the so-called formal exterior square L-function, when the Whittaker function is associated to a newform for π. By considerations on the Galois side, formal exterior square L-functions are equal to exterior square L-functions for some principal series representations.

scholarly journals Epsilon factors of symplectic type characters in the wild case

2021 ◽  
Vol 33 (2) ◽  
pp. 569-577
Author(s):  
Sazzad Ali Biswas
Keyword(s):  
Local Field ◽  
Characteristic Zero ◽  
Quadratic Extension ◽  
Multiplicative Character ◽  
In The Wild ◽  
Epsilon Factors

Abstract By work of John Tate we can associate an epsilon factor with every multiplicative character of a local field. In this paper, we determine the explicit signs of the epsilon factors for symplectic type characters of K × {K^{\times}} , where K / F {K/F} is a wildly ramified quadratic extension of a non-Archimedean local field F of characteristic zero.

Tempered Representations and the Theta Correspondence

1998 ◽  
Vol 50 (5) ◽  
pp. 1105-1118 ◽  
Author(s):  
Brooks Roberts
Keyword(s):  
Local Field ◽  
Nonnegative Integer ◽  
Characteristic Zero ◽  
Theta Correspondence

AbstractLet V be an even dimensional nondegenerate symmetric bilinear space over a nonarchimedean local field F of characteristic zero, and let n be a nonnegative integer. Suppose that σ ∈ Irr (O(V)) and π ∈ Irr (Sp(n, F)) correspond under the theta correspondence. Assuming that õ is tempered, we investigate the problem of determining the Langlands quotient data for π.

Solvable Points on Projective Algebraic Curves

2004 ◽  
Vol 56 (3) ◽  
pp. 612-637 ◽  
Author(s):  
Ambrus Pál
Keyword(s):  
Local Field ◽  
Characteristic Zero ◽  
Algebraic Curves ◽  
Residue Field ◽  
Rational Points ◽  
Projective Curve ◽  
Arbitrary Characteristic ◽  
Projective Curves ◽  
Solvable Extension ◽  
Solvable Points

AbstractWe examine the problem of finding rational points defined over solvable extensions on algebraic curves defined over general fields. We construct non-singular, geometrically irreducible projective curves without solvable points of genus g, when g is at least 40, over fields of arbitrary characteristic. We prove that every smooth, geometrically irreducible projective curve of genus 0, 2, 3 or 4 defined over any field has a solvable point. Finally we prove that every genus 1 curve defined over a local field of characteristic zero with residue field of characteristic p has a divisor of degree prime to 6p defined over a solvable extension.

Some Orbital Integrals and a Technique for Counting Representations of GL 2(F)

1978 ◽  
Vol 30 (02) ◽  
pp. 431-448 ◽  
Author(s):  
T. Callahan
Keyword(s):  
Haar Measure ◽  
Local Field ◽  
Maximal Ideal ◽  
Characteristic Zero ◽  
Maximal Compact Subgroup ◽  
Residue Field ◽  
Compact Subgroup ◽  
Orbital Integrals ◽  
Ring Of Integers

Let F be a local field of characteristic zero, with q elements in its residue field, ring of integers uniformizer ωF and maximal ideal . Let GF = GL2(F). We fix Haar measures dg and dz on GF and ZF, the centre of GF, so that meas(K) = meas where K = GL2() is a maximal compact subgroup of GF. If T is a torus in GF we take dt to be the Haar measure on T such that means(TM)=1 where TM denotes the maximal compact subgroup of T.

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