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On the convolution of Hecke L-functions

Published online by Cambridge University Press:  26 February 2010

B. Z. Moroz
B. Z. Moroz
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel.
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§1. Let k be an algebraic number field of finite degree over the field Q of rational numbers and Ki be an extension of k of degree (Ki:k) = ni, i = 1,2. We choose a Hecke Grössencharakter Xi in Ki and consider the L-function

associated with Xi see [1, 2]. It is known to be a meromorphic function on the whole complex plane. We are interested here in the properties of the convolution of functions LK1, LK2 over k defined by

where

and a (and n) run over integral ideals of Ki (and k), whose norm NKi/k a is equal to n. The function (2) is sometimes called the “scalar product of the Hecke L-functions” «3—11». The object of the paper is the following theorem.

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Type
Research Article
Information
Mathematika , Volume 27 , Issue 2 , December 1980 , pp. 312 - 320
Copyright
Copyright © University College London 1980

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References

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