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Subjects
11-XX Number theory
11Fxx Discontinuous groups and automorphic forms
11F66 Langlands $L$ -functions; one variable Dirichlet series and functional equations

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Displaying 1 – 20 of 161

A certain Dirichlet series attached to Siegel modular forms of degree two.

W. Kohnen, N.-P. Skoruppa (1989)

Inventiones mathematicae

A converse theorem for second-order modular forms of level N

Özlem Imamoglu, Yves Martin (2006)

Acta Arithmetica

A Dirichlet series for Hermitian modular forms of degree 2

S. Raghavan, J. Sengupta (1991)

Acta Arithmetica

A Dirichlet series for modular forms of degree n

Aloys Krieg (1991)

Acta Arithmetica

A mean square formula for central values of twisted automorphic L-functions

Yuk-Kam Lau, Kai-Man Tsang (2005)

Acta Arithmetica

A new multiple Dirichlet series induced by a higher-order form

Anton Deitmar, Nikolaos Diamantis (2010)

Acta Arithmetica

A note on average behaviour of the Fourier coefficients of $j$ th symmetric power $L$ -function over certain sparse sequence of positive integers

Youjun Wang (2024)

Czechoslovak Mathematical Journal

Let $j \geq 2$ be a given integer. Let $H_{k}^{*}$ be the set of all normalized primitive holomorphic cusp forms of even integral weight $k \geq 2$ for the full modulo group $SL (2, ℤ)$ . For $f \in H_{k}^{*}$ , denote by $λ_{{sym}^{j} f} (n)$ the $n$ th normalized Fourier coefficient of $j$ th symmetric power $L$ -function ( $L (s, {sym}^{j} f)$ ) attached to $f$ . We are interested in the average behaviour of the sum $\sum_{\binom{n = a_{1}^{2} + a_{2}^{2} + a_{3}^{2} + a_{4}^{2} + a_{5}^{2} + a_{6}^{2} \leq x}{(a_{1}, a_{2}, a_{3}, a_{4}, a_{5}, a_{6}) \in ℤ^{6}}} λ_{{sym}^{j} f}^{2} (n),$ where $x$ is sufficiently large, which improves the recent work of A. Sharma and A. Sankaranarayanan (2023).

A Rankin-Selberg integral for the adjoint representation of GL3.

David Ginzburg (1991)

Inventiones mathematicae

A remark on Construire un noyau de la fonctorialité by Lafforgue

Hervé Jacquet (2012)

Annales de l’institut Fourier

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.

Abelova cena v roce 2018 udělena za Langlandsův program

Vítězslav Kala (2018)

Pokroky matematiky, fyziky a astronomie

V článku motivujeme a vysvětlíme základy Langlandsova programu, sítě domněnek propojujících řadu různých oblastí matematiky. Během toho se také setkáme s Riemannovou hypotézou a domněnkou Birche a Swinnerton-Dyera, dvěma ze sedmi problémů tisíciletí vyhlášených Clayovým matematickým institutem.

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

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

Acta Arithmetica

Admissible $p$ -adic measures attached to triple products of elliptic cusp forms.

Böcherer, Siegfried, Panchishkin, A.A. (2007)

Documenta Mathematica

An application of the projections of $C^{\infty}$ automorphic forms

Takumi Noda (1995)

Acta Arithmetica

An orthogonal test of the L-functions Ratios Conjecture, II

Steven J. Miller, David Montague (2011)

Acta Arithmetica

Andrianov' s L-functions associated to Siegel wave forms of degree two.

Akira Hori (1995)

Mathematische Annalen

Artin formalism and heat kernels.

Serge Lang, Jay Jorgenson (1994)

Journal für die reine und angewandte Mathematik

Automorphic $L$ -functions in the weight aspect.

Fomenko, O.M. (2004)

Zapiski Nauchnykh Seminarov POMI

Bounds for automorphic L-functions.

H. Iwaniec, W. Duke, J. Frielander (1993)

Inventiones mathematicae

Bounds for automorphic L-functions. II.

H. Iwaniec, W. Duke, J.B. Firedlander (1994)

Inventiones mathematicae

Bounds for modular L-functions in the level aspect

Valentin Blomer, Gergely Harcos, Philippe Michel (2007)

Annales scientifiques de l'École Normale Supérieure

Currently displaying 1 – 20 of 161

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