We introduce p-adic L-functions and their main properties using Mazur's contruction and p-adic measures; we also discuss what is known and what is expected about the distribution of zeroes for both complex and p-adic L-functions. After this, we focus on the study of the Elienberg-Jain-Venkatesh conjecture (2011) about the zeroes of family of p-adic L-functions corresponding to imaginary quadratic fields; we support this study also by doing some numerical experiments on the lambda invariants and on the order of these zeroes.

Zeroes of p-adic L-functions: the Ellenberg-Jain-Venkatesh conjecture

Santato, Giacomo
2021/2022

Abstract

We introduce p-adic L-functions and their main properties using Mazur's contruction and p-adic measures; we also discuss what is known and what is expected about the distribution of zeroes for both complex and p-adic L-functions. After this, we focus on the study of the Elienberg-Jain-Venkatesh conjecture (2011) about the zeroes of family of p-adic L-functions corresponding to imaginary quadratic fields; we support this study also by doing some numerical experiments on the lambda invariants and on the order of these zeroes.
2021-07-21
58
p-adic L-functions, p-adic measures, Random matrices, Hazelgrave phenomenon, lambda invariant
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12608/21322