Journal articleAmerican Journal of Mathematics · June 1, 2025
Schubert Eisenstein series are defined by restricting the summation in a degenerate Eisenstein series to a particular Schubert variety. In the case of GL3 over ℚ Bump and the first author proved that these Schubert Eisenstein series have meromor ...
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Journal articleSelecta Mathematica New Series · April 1, 2025
We prove a Poisson summation formula for the zero locus of a quadratic form in an even number of variables with no assumption on the support of the functions involved. The key novelty in the formula is that all “boundary terms” are given either by constant ...
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Journal articleScience China Mathematics · June 1, 2021
Braverman and Kazhdan (2000) introduced influential conjectures aimed at generalizing the Fourier transform and the Poisson summation formula. Their conjectures should imply that quite general Langlands L-functions have meromorphic continuations and functi ...
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Journal articleAmerican Journal of Mathematics · October 1, 2020
Let F be a number field and let AF be its ring of adeles. Let B be a quaternion algebra over F and let ν: B → F be the reduced norm. Consider the reductive monoid M over F whose points in an F-algebra R are given by (Formula Presented). Motivate ...
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Journal articleAdvances in Mathematics · April 30, 2019
Let V 1 ,V 2 ,V 3 be a triple of even dimensional vector spaces over a number field F equipped with nondegenerate quadratic forms Q 1 ,Q 2 ,Q 3 , respectively. Let Y⊂∏i=1V i be th ...
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Journal articlePacific Journal of Mathematics · January 1, 2018
Braverman and Kazhdan have introduced an influential conjecture on local functional equations for general Langlands L-functions. It is related to L. Lafforgue's equally influential conjectural construction of kernels for functorial transfers. We formulate ...
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Journal articleResearch in Mathematical Sciences · December 1, 2016
Let F be a number field, let AF be its ring of adeles, and let g1, g2, h1, h2∈ GL 2(AF). We provide an absolutely convergent geometric expression for ∑πKπ(g1,g2)Kπ∨(h1,h2)Ress=1LS ...
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Journal articleResearch in Mathematical Sciences · December 1, 2015
Let E/F be an everywhere unramified extension of number fields with Gal(E/F) simple and nonabelian. In a recent paper, the first named author suggested an approach to nonsolvable base change and descent of automorphic representations of GL2 alon ...
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Journal articleProceedings of the American Mathematical Society · January 1, 2015
Let F be a number field and let π be a cuspidal unitary automorphic representation of GLmn(AF) where m and n are integers greater than one. We propose a conjecturally necessary condition for π to be a Rankin-Selberg transfer of an aut ...
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Journal articlePacific Journal of Mathematics · January 1, 2015
In this paper we prove a relative trace formula for all pairs of connected algebraic groups H ≤ G × G, with G a reductive group and H the direct product of a reductive group and a unipotent group, given that the test function satisfies simplifying hypothes ...
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Journal articleJournal of the Ramanujan Mathematical Society · 2012
We present a collection of conjectural trace identities and explain why they are
equivalent to base change and descent of automorphic representations of GL(n) along
nonsolvable extensions (under some simplifying hypotheses). The case n = 2 is treated in
mo ...
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Journal articleAmerican Journal of Mathematics · December 1, 2007
Let Script O sign be the ring of integers of a totally real number field E and set G := ResE/ℚ( GL2). Fix an ideal c ⊂ Script O sign. For each ideal m ⊂ Script O sign let T(m) denote the mth Hecke operator associated to the standard c ...
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Journal articleJournal of Mathematical Analysis and Applications · January 1, 2004
Let G-fraktur signp(x) ε double struck F sign p[x] be the polynomial whose zeros are the j-invariants of supersingular elliptic curves over double struck F signp. Generalizing a construction of Atkin described in a recent p ...
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Journal articleProceedings of the American Mathematical Society · January 1, 2004
Rankin and Swinnerton-Dyer (1970) prove that all zeros of the Eisenstein series Ek in the standard fundamental domain for Γ lie on A:= {eiθ:π/2 ≤ θ ≤ 2π/3}. In this paper we generalize their theorem, providing conditions under which t ...
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Journal articleJournal of Combinatorial Theory Series A · January 1, 2002
In the study of partition theory and q-series, identities that relate series to infinite products are of great interest (such as the famous Rogers-Ramanujan identities). Using a recent result of Zagier, we obtain an infinite family of such identities that ...
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