Bianchi modular symbols and $p$-adic $L$-functions

Abstract

In the present paper, we constructed the $p$-adic $L$-function of Bianchi modular form. Also we proved that the first homology groups are generated by the special Bianchi modular symbols. As a corollary, the $\mu$-invariant of some isotopic component of the $p$-adic $L$-function vanishes for Bianchi newforms and a positive proportion of ordinary primes. Also we obtain the residual non-vanishing result of the integral $L$-values.

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References in corpus (5)

• $P$-adic $L$-functions of Bianchi modular forms
• Families of Bianchi modular symbols: critical base-change p-adic L-functions and p-adic Artin formalism
• Modular symbols for reductive groups and p-adic Rankin-Selberg convolutions over number fields
• Genuine Bianchi modular forms of higher level, at varying weight and discriminant
• Non-vanishing of special $L$-values of cusp forms on GL(2) with totally split prime power twists