Eisenstein series in hyperbolic 3-space and Kronecker limit formula for biquadratic field

Let L = K be the composite of two imaginary quadratic fields and K. Suppose that the discriminants of and K are relatively prime. For any primitive ray class character χ of L, we shall compute L(1, χ) for the Hecke L-function in L. We write for the conductor of χ and C for the ray class modulo . Let...

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Bibliographic Details
Published in:Nagoya mathematical journal 1989-03, Vol.113, p.129-146
Main Author: Konno, Shuji
Format: Article
Language:English
Subjects:
11F30
11R42
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Summary:Let L = K be the composite of two imaginary quadratic fields and K. Suppose that the discriminants of and K are relatively prime. For any primitive ray class character χ of L, we shall compute L(1, χ) for the Hecke L-function in L. We write for the conductor of χ and C for the ray class modulo . Let c ε C be any integral ideal prime to . We write as g-module where g, n and ϑL are, respectively, the ring of integers in k, an ideal in k and the differente of L. Let where T(χ) is the Gaussian sum and, as in (3.2),
ISSN:0027-7630
2152-6842
DOI:10.1017/S002776300000129X