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The shifted fourth moment of automorphic L-functions of prime power level

Olga Balkanova (2016)

Acta Arithmetica

We prove an asymptotic formula for the fourth moment of automorphic L-functions of level $p^{ν}$ , where p is a fixed prime number and ν → ∞. This is a continuation of work by Rouymi, who computed the asymptotics of the first three moments at a prime power level, and a generalization of results obtained for a prime level by Duke, Friedlander Iwaniec and Kowalski, Michel VanderKam.

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

Yumiko Ichihara (2000)

Acta Arithmetica

The singular modular forms on the 27-dimensional exceptional domain.

Aloys Krieg (1997)

Manuscripta mathematica

The space of period polynomials

Shinji Fukuhara (1997)

Acta Arithmetica

The spectral growth of automorphic L-functions.

Henryk Iwaniec (1992)

Journal für die reine und angewandte Mathematik

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

M. Jutila (2004)

Publications de l'Institut Mathématique

The spectral mean value for linear forms in twisted coefficients of cusp forms

Wenzhi Luo (1995)

Acta Arithmetica

The Spectrum of Fermat Curves.

P. Sarnak, R. Philips (1991)

Geometric and functional analysis

The spt-crank for overpartitions

Frank G. Garvan, Chris Jennings-Shaffer (2014)

Acta Arithmetica

Bringmann, Lovejoy, and Osburn (2009, 2010) showed that the generating functions of the spt-overpartition functions $\bar{s p t} (n)$ , ${\bar{s p t}}_{1} (n)$ , ${\bar{s p t}}_{2} (n)$ , and M2spt(n) are quasimock theta functions, and satisfy a number of simple Ramanujan-like congruences. Andrews, Garvan, and Liang (2012) defined an spt-crank in terms of weighted vector partitions which combinatorially explain simple congruences modulo 5 and 7 for spt(n). Chen, Ji, and Zang (2013) were able to define this spt-crank in terms of ordinary partitions. In this...