Riemann hypothesis for period polynomials attached to the derivatives of L-functions of cusp forms for Γ0(N)

Riemann hypothesis for period polynomials attached to the derivatives of L-functions of cusp forms for Γ0(N)

We prove the Riemann hypothesis for the period polynomials attached to the first derivatives of L-functions of newforms f∈Sk(Γ0(N)) for all but finitely many pairs (k,N) of weight k and level N, as an extension of the results by Jin, Ma, Ono and Soundararajan [8] and by Diamantis and Rolen [4,5].

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Veröffentlicht in:Journal of mathematical analysis and applications 2022-05, Vol.509 (2), p.125971, Article 125971
Hauptverfasser: Im, Bo-Hae, Kim, Hojin
Format: Artikel
Sprache:eng
Schlagworte:
Cusp form
Hecke group
L-function
Period polynomial
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Zusammenfassung:We prove the Riemann hypothesis for the period polynomials attached to the first derivatives of L-functions of newforms f∈Sk(Γ0(N)) for all but finitely many pairs (k,N) of weight k and level N, as an extension of the results by Jin, Ma, Ono and Soundararajan [8] and by Diamantis and Rolen [4,5].
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2021.125971