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Published online by Cambridge University Press:  14 October 2021

School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield, S3 7RH, UK e-mail:


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.

Research Article
© The Author(s), 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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