On certain partial sums involving squares of Hecke eigenvalues

Winfried Kohnen; Florian Luca

doi:10.46298/hrj.2024.13031

Winfried Kohnen ; Florian Luca - On certain partial sums involving squares of Hecke eigenvalues

hrj:13031 - Hardy-Ramanujan Journal, February 10, 2024, Volume 46 - 2023 - https://doi.org/10.46298/hrj.2024.13031

On certain partial sums involving squares of Hecke eigenvaluesArticle

Authors: Winfried Kohnen ¹; Florian Luca

1 Universität Heidelberg [Heidelberg] = Heidelberg University

Let $a(n)$ be the $n$ th Fourier coefficient of a cuspidal Hecke eigenform of even integral weight $k\ge 2$ and trivial character that is a normalized new form for some level $N$ . We show that the partial sums

$H_n=\sum_{m=1}^n a(m)^2/m^k$ are not integral for

$n\ge n_0$ .

https://doi.org/10.46298/hrj.2024.13031

Source: HAL:hal-04442692v1

Volume: Volume 46 - 2023

Published on: February 10, 2024

Accepted on: February 10, 2024

Submitted on: February 9, 2024

Keywords: Fourier coefficients of automorphic forms,11F30, 11F11, 11N36,[MATH]Mathematics [math]

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Mathematics Subject Classification 2020¹

Sources:

[1] zbMATH Open.

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Review available on zbMATH Open, by David Lowry-Duda (Providence) (English)

1 zbMATH Open

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