Critical Values of Symmetric Power L-functions

Neil Dummigan, Mark E. Watkins

Type: Article

Publication Date: 2009-01-01

Citations: 3

DOI: https://doi.org/10.4310/pamq.2009.v5.n1.a4

Abstract

We consider the critical values of symmetric power L-functions attached to elliptic curves over Q.We show how to calculate a canonical Deligne period, and in several numerical examples, especially for sixth and tenth powers, we examine the factorisation of the rational number apparently obtained when one divides the critical value by the canonical period.This seems to provide some support for the Bloch-Kato conjecture, when we compare it with calculations and bounds for Tamagawa factors and global torsion terms.For large odd powers (5th-9th), we see several examples fitting well with the squareness of the order of the Shafarevich-Tate group.

Locations

Pure and Applied Mathematics Quarterly - View - PDF

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+	Polynomial Invariants of Finite Groups	1995	Larry Smith
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+	Modular forms whose fourier coefficients involve zeta-functions of quadratic fields	1977	Don Zagier
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+	Propri�t�s galoisiennes des points d'ordre fini des courbes elliptiques	1971	Jean-Pierre Serre
+	Rational isogenies of prime degree	1978	Barry Mazur Dorian Goldfeld
+	Cuspidality of symmetric powers with applications	2002	Henry H. Kim Freydoon Shahidi