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

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84097

Title: SOME SIEGEL MODULAR STANDARD L-VALUES, AND SHAFAREVICH-TATE GROUPS
Authors: Dummigan, Neil Browse this author
Ibukiyama, Tomoyoshi Browse this author
Katsurada, Hidenori Browse this author
Issue Date: 23-Oct-2009
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 950
Start Page: 1
End Page: 35
Abstract: 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.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69757
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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