Special values of symmetric power L-functions and Hecke eigenvalues
نویسندگان
چکیده
منابع مشابه
Critical Values of Symmetric Power L-functions
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...
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Introduction. The Fourier coefficients of modular forms of even integer weight on the full modular group SL(2,Z) can by now be considered classical in number theory. Among their intriguing properties appears a remarkable congruence of Ramanujan τ(n) ≡ σ11(n) mod 691. Plenty of excellent works, such as [9], [10], [12] and [13], that appeared in the last two decades were devoted to various genera...
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Let K be an imaginary quadratic eld and let O be the ring of integers of K. Let E be an elliptic curve deened over Q with complex multiplication by O. Let be the Grr ossencharacter attached to the curve E over K by the theory of complex multiplication, and let L(k ; s) be the complex Hecke L-function attached to the powers of , k = 1; 2; ; here we have xed an embedding of K in C. In a previous ...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2007
ISSN: 1246-7405
DOI: 10.5802/jtnb.609