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L-Series for genera at s = 1

Published online by Cambridge University Press:  26 February 2010

Kenneth H. Rosen
Kenneth H. Rosen
Affiliation:
Department of Mathematics, The University of Maine, Orono, Maine 04469, U.S.A.
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Abstract

It has been conjectured that, if p ≡ 1 (mod 4) is prime, and if d < 0 is a square-free discriminant with then

Where belongs to the field is the fundamental unit of Q(√k), depending on whether there are an even number or an odd number of classes per genus in Q(√d), and Ω is the genus field of Q(√d). Here the summation being over a complete set of inequivalent forms in the genus G, and

In this paper it will be shown that this conjecture is true when d is the product of two odd discriminants. An example when d is the product of three prime discriminants is discussed.

Type
Research Article
Information
Mathematika , Volume 27 , Issue 1 , June 1980 , pp. 10 - 16
Copyright
Copyright © University College London 1980

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