Non-random behavior in sums of modular symbols

DOI10.1142/S1793042122500464zbMath1493.11090arXiv1905.10743OpenAlexW3212627706WikidataQ114071919 ScholiaQ114071919MaRDI QIDQ5863780

Alex Cowan

Publication date: 3 June 2022

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.10743

zbMATH Keywords

Eisenstein seriesautomorphic formsmodular symbolsspectral theory of automorphic forms

Mathematics Subject Classification ID

Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36)

Uses Software

• LMFDB
• GL(n)pack
• ecdata

Cites Work

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• Fourier coefficients of Eisenstein series formed with modular symbols and their spectral decomposition
• The Selberg trace formula for \(\text{PSL}(2,\mathbb R)\). Vol. 2
• On convolutions of non-holomorphic Eisenstein series
• Coefficients of Maass forms and the Siegel zero. Appendix: An effective zero-free region, by Dorian Goldfeld, Jeffrey Hoffstein and Daniel Lieman
• Estimating additive character sums for Fuchsian groups
• Arithmetic statistics of modular symbols
• Explicit calculations with Eisenstein series
• Modular symbols have a normal distribution
• Bounds for the torsion of elliptic curves over number fields
• Central values of additive twists of cuspidal \(L\)-functions
• Non-real poles and irregularity of distribution
• On the Vanishing of TwistedL-Functions of Elliptic Curves
• Properties of Eisenstein series formed with modular symbols
• Automorphic Forms and L-Functions for the GroupGL(n, R)

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