Geodesic
CONGRUENCES OF SAITO–KUROKAWA LIFTS AND DENOMINATORS OF CENTRAL SPINOR L-VALUES
Glasgow mathematical journal, Tome 64 (2022) no. 2, pp. 504-525

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DOI

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. 
DUMMIGAN, NEIL. CONGRUENCES OF SAITO–KUROKAWA LIFTS AND DENOMINATORS OF CENTRAL SPINOR L-VALUES. Glasgow mathematical journal, Tome 64 (2022) no. 2, pp. 504-525. doi: 10.1017/S0017089521000331
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     title = {CONGRUENCES {OF} {SAITO{\textendash}KUROKAWA} {LIFTS} {AND} {DENOMINATORS} {OF} {CENTRAL} {SPINOR} {L-VALUES}},
     journal = {Glasgow mathematical journal},
     pages = {504--525},
     year = {2022},
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