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An Elementary Proof of a Weak Exceptional Zero Conjecture

Published online by Cambridge University Press:  20 November 2018

Louisa Orton
Louisa Orton*
Affiliation:
NWF I-Mathematik, Universität Regensburg, 93040 Regensburg, Germany e-mail: louisa.orton@mathematik.uni-regensburg.de
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Abstract

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In this paper we extend Darmon's theory of “integration on ${{\text{H}}_{p}}\times \text{H}$” to cusp forms $f$ of higher even weight. This enables us to prove a “weak exceptional zero conjecture”: that when the $p$-adic $L$-function of $f$ has an exceptional zero at the central point, the $\mathcal{L}$-invariant arising is independent of a twist by certain Dirichlet characters.

Keywords

11F1111F67
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 56 , Issue 2 , 01 April 2004 , pp. 373 - 405
Copyright
Copyright © Canadian Mathematical Society 2004

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