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Hecke Operators and Derivatives of L-Functions

Published online by Cambridge University Press:  04 December 2007

Nikolaos Diamantis
Nikolaos Diamantis
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germany. E-mail: diamant@mpim-bonn.mpg.de
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Abstract

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In this paper, we introduce a new way of studying derivatives of L-functions of cusp forms by associating to them cocycles analogous, in function, to the period polynomial. The main result gives a description of the effect of Hecke operators on these cocycles.

Keywords

cusp formsL-functionsderivativescocyclesperiodsperiod polynomialEichler–Shimura relationsHecke operators
Type
Research Article
Information
Compositio Mathematica , Volume 125 , Issue 1 , January 2001 , pp. 39 - 54
Copyright
© 2001 Kluwer Academic Publishers