Bounds for integral moments of quadratic twists of Fourier coefficients of modular forms

In this paper, we obtain under the assumption of the Generalized Riemann Hypothesis upper bounds for all high integral moments of sums of Fourier coefficients of a given modular form twisted by quadratic Dirichlet characters. We show the bounds are optimal by establishing unconditionally the corresponding lower bounds for all even integer moments.

Publication Details

Journal
ArXiv.org
Published
2025-09-24
Primary Topic
Geochemistry and Geologic Mapping
Type
article
Field-Weighted Citation Impact
0.00
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

Bounds for integral moments of quadratic twists of Fourier coefficients of modular forms

ArXiv.org
Geochemistry and Geologic Mapping
article

Bounds for integral moments of quadratic twists of Fourier coefficients of modular forms

article en

Abstract

In this paper, we obtain under the assumption of the Generalized Riemann Hypothesis upper bounds for all high integral moments of sums of Fourier coefficients of a given modular form twisted by quadratic Dirichlet characters. We show the bounds are optimal by establishing unconditionally the corresponding lower bounds for all even integer moments.

ArXiv.org
Openalex Percentile: Top 26%
Geochemistry and Geologic Mapping
Open Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

Bounds for integral moments of quadratic twists of Fourier coefficients of modular forms · ArXiv.org (2025) | TGRS Research Map | TGRS