pp-adic L-functions of automorphic forms and exceptional zeros

  • Holger Deppe

$p$-adic L-functions of automorphic forms and exceptional zeros cover
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Abstract

We construct pp-adic L-functions for automorphic representations of \GL\GL_2 of a number field FF , and show that the corresponding pp-adic L-function of a modular elliptic curve EE over FF has an extra zero at the central point for each prime above pp at which EE has split multiplicative reduction, a part of the exceptional zero conjecture.

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Holger Deppe, pp-adic L-functions of automorphic forms and exceptional zeros. Doc. Math. 21 (2016), pp. 689–734

DOI 10.4171/DM/543