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

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 $n\ge n_0$.


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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