Bounds on shifted convolution sums for Hecke eigenforms

Asbjørn C. Nordentoft; Yiannis N. Petridis; Morten S. Risager

doi:10.1007/s40993-022-00320-1

Bounds on shifted convolution sums for Hecke eigenforms

Asbjørn C. Nordentoft, Yiannis N. Petridis^*, Morten S. Risager

^*Corresponding author for this work

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

3 Citations (Scopus)

27 Downloads (Pure)

Abstract

Shifted convolution sums play a prominent rôle in analytic number theory. Here these sums are considered in the context of holomorphic Hecke eigenforms. We investigate pointwise bounds, mean-square bounds consistent with the optimal conjectural bound, and find asymptotics on average for their variance.

Original language	English
Article number	26
Journal	Research in Number Theory
Volume	8
Issue number	2
Pages (from-to)	1-20
ISSN	2363-9555
DOIs	https://doi.org/10.1007/s40993-022-00320-1
Publication status	Published - 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s).

Keywords

Shifted convolution sums

Access to Document

10.1007/s40993-022-00320-1Licence: CC BY

FulltextFinal published version, 394 KBLicence: CC BY

Cite this

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title = "Bounds on shifted convolution sums for Hecke eigenforms",

abstract = "Shifted convolution sums play a prominent r{\^o}le in analytic number theory. Here these sums are considered in the context of holomorphic Hecke eigenforms. We investigate pointwise bounds, mean-square bounds consistent with the optimal conjectural bound, and find asymptotics on average for their variance.",

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AU - Petridis, Yiannis N.

AU - Risager, Morten S.

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AB - Shifted convolution sums play a prominent rôle in analytic number theory. Here these sums are considered in the context of holomorphic Hecke eigenforms. We investigate pointwise bounds, mean-square bounds consistent with the optimal conjectural bound, and find asymptotics on average for their variance.

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DO - 10.1007/s40993-022-00320-1

M3 - Journal article

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