Dummigan, N. (2022) Congruences of Saito-Kurokawa lifts and denominators of central spinor L-values. Glasgow Mathematical Journal, 64 (2). pp. 504-525. ISSN 0017-0895
Abstract
Following Ryan and Tornaría, we prove that moduli of congruences of Hecke eigenvalues, between Saito–Kurokawa lifts and non-lifts (certain Siegel modular forms of genus 2), occur (squared) in denominators of central spinor L-values (divided by twists) for the non-lifts. This is conditional on Böcherer’s conjecture and its analogues and is viewed in the context of recent work of Furusawa, Morimoto and others. It requires a congruence of Fourier coefficients, which follows from a uniqueness assumption or can be proved in examples. We explain these factors in denominators via a close examination of the Bloch–Kato conjecture.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust. This is an author produced version of a paper subsequently published in Glasgow Mathematical Journal. Article available under the terms of the CC-BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/). |
Keywords: | 11F46; 11F33; 11F67 |
Dates: |
|
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: | 27 Sep 2021 15:38 |
Last Modified: | 07 Jul 2022 13:19 |
Status: | Published |
Publisher: | Cambridge University Press (CUP) |
Refereed: | Yes |
Identification Number: | 10.1017/S0017089521000331 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:178315 |