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Displaying 1 – 17 of 17

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

The Mean Square of Dirichlet Series Associated with Automorphic Forms.

Wolfgang Müller (1992)

Monatshefte für Mathematik

The prime number theorem in short intervals for automorphic L-functions

Y. Qu, J. Wu (2012)

Acta Arithmetica

The q-Mellin transform of automorphic forms and converse theorems

Mitsugu Mera (2008)

Acta Arithmetica

The second moment of Dirichlet twists of Hecke L-functions

Peng Gao, Rizwanur Khan, Guillaume Ricotta (2009)

Acta Arithmetica

The second moment of quadratic twists of modular L-functions

K. Soundararajan, Matthew P. Young (2010)

Journal of the European Mathematical Society

We study the second moment of the central values of quadratic twists of a modular $L$ -function. Unconditionally, we obtain a lower bound which matches the conjectured asymptotic formula, while on GRH we prove the asymptotic formula itself.

Currently displaying 1 – 17 of 17

Page 1

Displaying 1 – 17 of 17

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

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

The distribution of Fourier coefficients of cusp forms over sparse sequences

The local Jacquet-Langlands correspondence via Fourier analysis

The Maaß Space and Hecke Operators.

The Mean Square of Dirichlet Series Associated with Automorphic Forms.

The prime number theorem in short intervals for automorphic L-functions

The q-Mellin transform of automorphic forms and converse theorems

The second moment of Dirichlet twists of Hecke L-functions

The second moment of quadratic twists of modular L-functions

The second moment of the symmetric square $L$ -functions.

The Siegel-Walfisz theorem for Rankin-Selberg L-functions associated with two cusp forms

The spectral growth of automorphic L-functions.

The Spectral Mean Square of Hecke L-functions on the Critical Line

The universality of zeta-functions attached to certain cusp forms

Theta and L-function splittings

Theta-transforms and even zeta functions of Siegel modular forms

Currently displaying 1 – 17 of 17