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Displaying 101 – 120 of 161

Quadratic modular symbols on Shimura curves

Pilar Bayer, Iván Blanco-Chacón (2013)

Journal de Théorie des Nombres de Bordeaux

We introduce the concept of quadratic modular symbol and study how these symbols are related to quadratic $p$ -adic $L$ -functions. These objects were introduced in [3] in the case of modular curves. In this paper, we discuss a method to attach quadratic modular symbols and quadratic $p$ -adic $L$ -functions to more general Shimura curves.

Quantum ergodicity of Eigenfunctions on $P S L_{2} (𝐙) / 𝐇^{2}$

Wenzhi Luo, Peter Sarnak (1995)

Publications Mathématiques de l'IHÉS

Quantum unique ergodicity for Eisenstein series on $P S L_{2} (ℤ ∖ P S L_{2} (ℝ)$

Dmitry Jakobson (1994)

Annales de l'institut Fourier

In this paper we prove microlocal version of the equidistribution theorem for Wigner distributions associated to Eisenstein series on $P S L_{2} (ℤ) ∖ P S L_{2} (ℝ)$ . This generalizes a recent result of W. Luo and P. Sarnak who proves equidistribution for $P S L_{2} (ℤ) ∖ ℍ$ . The averaged versions of these results have been proven by Zelditch for an arbitrary finite-volume surface, but our proof depends essentially on the presence of Hecke operators and works only for congruence subgroups of $S L_{2} (ℝ)$ . In the proof the key estimates come from applying...

Quantum variance for Hecke eigenforms

Wenzhi Luo, Peter Sarnak (2004)

Annales scientifiques de l'École Normale Supérieure

Ramanujan identities and Euler products for a type of Dirichlet series

Zhi-Hong Sun, Kenneth S. Williams (2006)

Acta Arithmetica

Random matrix theory and the Fourier coefficients of half-integral weight forms.

Conrey, J.B., Keating, Jonathan P., Rubinstein, M.O., Snaith, N.C. (2006)

Experimental Mathematics

Rankin-Selberg method for real analytic cusp forms of arbitrary real weight.

Roland Matthes (1992)

Mathematische Zeitschrift

Répartition des zéros des fonctions $L$ et matrices aléatoires

Philippe Michel (2000/2001)

Séminaire Bourbaki

Shintani function and its application to automorphic L-functions for classical groups. I. The case of orthogonal groups.

Atsushi Murase, Takashi Sugano (1994)

Mathematische Annalen

Simple zeros of degree 2 $L$ -functions

Andrew R. Booker (2016)

Journal of the European Mathematical Society

We prove that the complete $L$ -functions of classical holomorphic newforms have infinitely many simple zeros.

Small gaps in coefficients of $L$ -functions and $m a t h f r a k B$ -free numbers in short intervals.

E. Kowalski, O. Robert, J. Wu (2007)

Revista Matemática Iberoamericana

Some results on reducibilty for unitary groups and local Asai L-functions.

David Goldberg (1994)

Journal für die reine und angewandte Mathematik

Sur les séries $L$ associées aux formes modulaires

Ha Huy Khoai (1992)

Bulletin de la Société Mathématique de France

Symétries spectrales des fonctions zêtas

Frédéric Paugam (2009)

Journal de Théorie des Nombres de Bordeaux

On définit, en réponse à une question de Sarnak dans sa lettre a Bombieri [Sar01], un accouplement symplectique sur l’interprétation spectrale (due à Connes et Meyer) des zéros de la fonction zêta. Cet accouplement donne une formulation purement spectrale de la démonstration de l’équation fonctionnelle due à Tate, Weil et Iwasawa, qui, dans le cas d’une courbe sur un corps fini, correspond à la démonstration géométrique usuelle par utilisation de l’accouplement de dualité de Poincaré Frobenius-équivariant...

Symmetric cube $L$ -functions for ${GL}_{2}$ are entire.

Kim, Henry H., Shahidi, Freydoon (1999)

Annals of Mathematics. Second Series

The arithmetic of the coefficients of half-integral weight Eisenstein series

Antal Balog, William J. McGraw, Ken Ono (2003)

Acta Arithmetica

The Dirichlet series of Koecher and Maaß and modular forms of weight 3/2.

Siegfried Böcherer, R. Schulze-Pillot (1992)

Mathematische Zeitschrift

The distribution of Fourier coefficients of cusp forms over sparse sequences

Huixue Lao, Ayyadurai Sankaranarayanan (2014)

Acta Arithmetica

Let $λ_{f} (n)$ be the nth normalized Fourier coefficient of a holomorphic Hecke eigenform $f (z) \in S_{k} (Γ)$ . We establish that $\sum_{n \leq x} λ_{f}^{2} (n^{j}) = c_{j} x + O (x^{1 - 2 / ({(j + 1)}^{2} + 1)})$ for j = 2,3,4, which improves the previous results. For j = 2, we even establish a better result.

The local Jacquet-Langlands correspondence via Fourier analysis

Jared Weinstein (2010)

Journal de Théorie des Nombres de Bordeaux

Let $F$ be a locally compact non-Archimedean field, and let $B / F$ be a division algebra of dimension 4. The Jacquet-Langlands correspondence provides a bijection between smooth irreducible representations $π^{'}$ of $B^{\times}$ of dimension $> 1$ and irreducible cuspidal representations of ${GL}_{2} (F)$ . We present a new construction of this bijection in which the preservation of epsilon factors is automatic. This is done by constructing a family of pairs $(ℒ, ρ)$ , where $ℒ \subset M_{2} (F) \times B$ is an order and $ρ$ is a finite-dimensional representation of a certain...

The Maaß Space and Hecke Operators.

Aloys Krieg (1990)

Mathematische Zeitschrift

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