SOME SIEGEL MODULAR STANDARD L-VALUES, AND SHAFAREVICH-TATE GROUPS

Dummigan, Neil; Ibukiyama, Tomoyoshi; Katsurada, Hidenori

Hokkaido University Preprint Series in Mathematics, 2009, 950, 1-35

Permalink : https://doi.org/10.14943/84097

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DOI	https://doi.org/10.14943/84097
URI	https://hdl.handle.net/2115/69757
タイトル	SOME SIEGEL MODULAR STANDARD L-VALUES, AND SHAFAREVICH-TATE GROUPS
著者	Dummigan, Neil ; Ibukiyama, Tomoyoshi ; Katsurada, Hidenori
著者名 Dummigan, Neil
著者名 Ibukiyama, Tomoyoshi
著者名 Katsurada, Hidenori
言語	英語
発行日	2009-10-23
出版者	Department of Mathematics, Hokkaido University
収録物名	Hokkaido University Preprint Series in Mathematics
巻(号)	950
ページ	1-35
抄録	We explain how the Bloch-Kato conjecture leads us to the following conclusion: a large prime dividing a critical value of the L-function of a classical Hecke eigenform f of level 1, should often also divide certain ratios of critical values for the standard L-function of a related genus two (and in general vector-valued) Hecke eigenform F. The relation between f and F (Harder’s conjecture in the vector-valued case) is a congruence involving Hecke eigenvalues, modulo the large prime. In the scalar-valued case we prove the divisibility, subject to weak conditions. In two instances in the vector-valued case, we confirm the divisibility using elaborate computations involving special differential operators. These computations do not depend for their validity on any unproved conjecture.
資源タイプ	紀要論文
出版タイプ	Version of Record