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

Published online by Cambridge University Press:  22 January 2016

Shuji Konno
Shuji Konno*
Affiliation:
Kobe Women’s College of Pharmacy, Motoyama Kitamachi 4-19-1 Higashinada-ku, Kobe 657, Japan
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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),

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 113 , March 1989 , pp. 129 - 146
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1989

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