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Algebra i Analiz, 2022, Volume 34, Issue 6, Pages 55–134 (Mi aa1837)  
Research Papers

On extra zeros of $p$-adic Rankin–Selberg $L$-functions

D. Benoisa, S. Horteb

a Institut de Mathématiques Université de Bordeaux 351, cours de la Libération, 33405 Talence, France
b 28, rue des Platanes 92500 Rueil-Malmaison, France
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Abstract: A version of the extra-zero conjecture, formulated by the first named author, is proved for $p$-adic $L$-functions associated with Rankin–Selberg convolutions of modular forms of the same weight. This result provides an evidence in support of this conjecture in the noncritical case, which remained essentially unstudied.
Keywords: $p$-adic $L$-functions, modular forms, $p$-adic representations.
Funding agency Grant number
Agence Nationale de la Recherche ANR-18-CE40-0029
The work of the first named author was partially supported by the Agence National de Recherche (grant ANR-18-CE40-0029) in the framework of the ANR-FNR project "Galois representations, automorphic forms and their $L$-functions".
Received: 14.08.2021
English version:
St. Petersburg Mathematical Journal, 2023, Volume 34, Issue 6, Pages 929–989
DOI: https://doi.org/10.1090/spmj/1785
Document Type: Article
Language: English
Citation: D. Benois, S. Horte, “On extra zeros of $p$-adic Rankin–Selberg $L$-functions”, Algebra i Analiz, 34:6 (2022), 55–134; St. Petersburg Math. J., 34:6 (2023), 929–989
Citation in format AMSBIB
\Bibitem{BenHor22}
\by D.~Benois, S.~Horte
\paper On extra zeros of $p$-adic Rankin--Selberg $L$-functions
\jour Algebra i Analiz
\yr 2022
\vol 34
\issue 6
\pages 55--134
\mathnet{http://mi.mathnet.ru/aa1837}
\transl
\jour St. Petersburg Math. J.
\yr 2023
\vol 34
\issue 6
\pages 929--989
\crossref{https://doi.org/10.1090/spmj/1785}
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