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Harder's conjecture and ratios of standard L-values

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Speaker: 
Neil Dummigan
Affiliation: 
Sheffield
Date: 
Wed, 2010-02-17 14:15 - 15:15
Location: 
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

I will explain how the Bloch-Kato conjecture leads to the following conclusion: any large prime dividing a critical value of the L-function of a classical Hecke eigenform of level 1, should also divide a certain ratio of critical values for the standard L-function of a related genus 2 (and in general vector-valued) Hecke eigenform F. This can be proved in the scalar-valued case, and there is experimental evidence in the vector-valued case (where the relation between f and F is a congruence of Hecke eigenvalues conjectured by Harder).

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