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Lafforgue has proposed a new approach to the principle of functoriality in a test case, namely, the case of automorphic induction from an idele class character of a quadratic extension. For technical reasons, he considers only the case of function fields and assumes the data is unramified. In this paper, we show that his method applies without these restrictions. The ground field is a number field or a function field and the data may be ramified.

A remark on my paper "On the Saito-Kurokawa lifting".

I.I. Piatetski-Shapiro (1984)

Inventiones mathematicae

Action of Hecke operators on products of Igusa theta constants with rational characteristics

Anatoli N. Andrianov, Fedor A. Andrianov (2004)

Acta Arithmetica

Algebraische Eigenschaften der lokalen Ringe in den Spitzen der Hilbertschen Modulgruppen.

Reinhardt Kiehl, Eberhard Freitag (1974)

Inventiones mathematicae

An analogue of the Weil representation for G2.

Gordan Savin (1993)

Journal für die reine und angewandte Mathematik

An Arithmetic of Hermitian Modular Forms of Degree Two.

Hisashi Kojima (1982)

Inventiones mathematicae

An Elementary Approach to Hecke Operators.

Erik Lippa (1973)

Mathematische Annalen

An inequality for local unitary Theta correspondence

Z. Gong, L. Grenié (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

Given a representation $π$ of a local unitary group $G$ and another local unitary group $H$ , either the Theta correspondence provides a representation $θ_{H} (π)$ of $H$ or we set $θ_{H} (π) = 0$ . If $G$ is fixed and $H$ varies in a Witt tower, a natural question is: for which $H$ is $θ_{H} (π) \neq 0$ ? For given dimension $m$ there are exactly two isometry classes of unitary spaces that we denote $H_{m}^{\pm}$ . For $ε \in {0, 1}$ let us denote $m_{ε}^{\pm} (π)$ the minimal $m$ of the same parity of $ε$ such that $θ_{H_{m}^{\pm}} (π) \neq 0$ , then we prove that $m_{ε}^{+} (π) + m_{ε}^{-} (π) \geq 2 n + 2$ where $n$ is the dimension of $π$ .

Analyse spectrale des formes automorphes et séries d'Eisenstein.

Gilles Lachaud (1978)

Inventiones mathematicae

Announcement of errors in "The Eichler Commutation Relation for theta series with spherical harmonics" (Acta Arith. 63 (1993), 233-254)

Lynne H. Walling (1994)

Acta Arithmetica

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A class of conjectured series representations for $1 / π$ .

A Dirichlet Series Associated to Eisenstein Series of Degree Two.

A Hyperbolic Kac-Moody Algebra and the Theory of Siegel Modular Forms of Genus 2.

A new way to get Euler products.

A Non-Vanishing Theorem for Zeta Functions of GLn

A note on fields of definition

A relation between automorphic representations of $GL (2)$ and $GL (3)$

A remark on Construire un noyau de la fonctorialité by Lafforgue

A remark on my paper "On the Saito-Kurokawa lifting".

Action of Hecke operators on products of Igusa theta constants with rational characteristics

Algebraische Eigenschaften der lokalen Ringe in den Spitzen der Hilbertschen Modulgruppen.

An analogue of the Weil representation for G2.

An Arithmetic of Hermitian Modular Forms of Degree Two.

An Elementary Approach to Hecke Operators.

An inequality for local unitary Theta correspondence

Analyse spectrale des formes automorphes et séries d'Eisenstein.

Announcement of errors in "The Eichler Commutation Relation for theta series with spherical harmonics" (Acta Arith. 63 (1993), 233-254)

Anticyclotomic main conjectures.

Appendix to Orloff: Critical values of certain tensor product L-functions.

Applications of special functions for the general linear group to number theory

Currently displaying 1 – 20 of 25