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arXiv · 1311.6168

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

Holger Deppe
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Abstract

Let F be a number field, p a prime number. We construct the (multi-variable) p-adic L-function of an automorphic representation of $GL_2(A_F)$ (with certain conditions at places above p and $\infty$), which interpolates the complex L-function at the central critical point. We use this construction to prove that the p-adic L-function of a modular elliptic curve E over F has vanishing order greater or equal to the number of primes above p at which E has split multiplicative reduction, as predicted by the exceptional zero conjecture. This is a generalization of analogous results by Spieß (arXiv:1207.2289) over totally real fields.

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Holger Deppe. 2013-11-29. p-adic L-functions of automorphic forms and exceptional zeros. https://arxiv.org/abs/1311.6168

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