Dummigan, N., Heim, B. and Rendina, A. (2018) Kurokawa–Mizumoto congruences and degree-8 L-values. Manuscripta Mathematica. ISSN 0025-2611
Abstract
Let f be a Hecke eigenform of weight k, level 1, genus 1. Let E2,1k(f) be its genus-2 Klingen–Eisenstein series. Let F be a genus-2 cusp form whose Hecke eigenvalues are congruent modulo q to those of E2,1k(f), where q is a “large” prime divisor of the algebraic part of the rightmost critical value of the symmetric square L-function of f. We explain how the Bloch–Kato conjecture leads one to believe that q should also appear in the denominator of the “algebraic part” of the rightmost critical value of the tensor product L-function L(s, f⊗ F) , i.e. in an algebraic ratio obtained from the quotient of this with another critical value. Using pullback of a genus-5 Siegel–Eisenstein series, we prove this, under weak conditions.
Metadata
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Copyright, Publisher and Additional Information: | © Springer-Verlag GmbH Germany, part of Springer Nature 2018. This is an author produced version of a paper subsequently published in manuscripta mathematica. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at Springer via https://doi.org/10.1007/s00229-018-1061-9. |
Keywords: | 11F33; 11F46; 11F67; 11F80 |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 05 Sep 2018 11:46 |
Last Modified: | 06 Aug 2019 00:39 |
Published Version: | https://doi.org/10.1007/s00229-018-1061-9 |
Status: | Published online |
Publisher: | Springer Verlag |
Refereed: | Yes |
Identification Number: | https://doi.org/10.1007/s00229-018-1061-9 |