On standard L-functions for E6 and E7.
David Ginzburg (1995)
Journal für die reine und angewandte Mathematik
Aleksandar Ivić (2001)
Journal de théorie des nombres de Bordeaux
We have for is the first Fourier coefficient of the Maass wave form corresponding to the eigenvalue to which the Hecke series is attached. This result yields the new bound
Hidenori Katsurada, Hisa-aki Kawamura (2010)
Acta Arithmetica
Besser, Amnon (1997)
Documenta Mathematica
Yujiao Jiang, Guangshi Lü (2014)
Acta Arithmetica
Let be the nth normalized Fourier coefficient of a holomorphic or Maass cusp form f for SL(2,ℤ). We establish the asymptotic formula for the summatory function as x → ∞, where q grows with x in a definite way and j = 2,3,4.
Guodong Hua (2022)
Czechoslovak Mathematical Journal
Let be a normalized primitive holomorphic cusp form of even integral weight for the full modular group . Denote by the th normalized Fourier coefficient of . We are interested in the average behaviour of the sum for , where and is any fixed positive integer. In a similar manner, we also establish analogous results for the normalized coefficients of Dirichlet expansions of associated symmetric power -functions and Rankin-Selberg -functions.
Tamotsu Ikeda (1992)
Compositio Mathematica
Kohji Matsumoto (1991)
Acta Arithmetica
Henryk Iwaniec (1990)
Journal de théorie des nombres de Bordeaux
Tamotsu Ikeda (1996)
Compositio Mathematica
Solomon Friedberg, Shek-Tung Wong (1991)
Mathematische Annalen
Yuval Z. Flicker (1993)
Mathematische Annalen
A. Laurinčikas, J. Steuding (2004)
Open Mathematics
In the paper the asymptotics for Dirichlet polynomials associated to certain cusp forms are obtained.
Antanas Laurinčikas, Joern Steuding, Darius Šiaučiūnas (2009)
Open Mathematics
A formula for the mean value of multiplicative functions associated to certain cusp forms is obtained. The paper is a continuation of [4].
Liangyi Zhao (2006)
Revista Matemática Iberoamericana
In this paper, we are interested in exploring the cancellation of Hecke eigenvalues twisted with an exponential sums whose amplitude is √n at prime arguments.
E. Royer (2001)
Acta Arithmetica
Shin-ichiro Mizumoto (1991)
Mathematische Annalen
J. Wu (2009)
Acta Arithmetica
Roland Matthes (1994)
Journal für die reine und angewandte Mathematik
Lionel Fourquaux (2002)
Journal de théorie des nombres de Bordeaux
Considérons les formes linéaires sur l’espace vectoriel des formes paraboliques de poids pour le groupe de congruence , avec un caractère de Dirichlet modulo . Par le produit scalaire de Petersson, on peut leur associer des formes paraboliques. Cet article détermine le produit scalaire de deux de ces formes, pour deux caractères de Dirichlet non triviaux de parités différentes.