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arXiv · 2108.05592

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

Jaesung Kwon
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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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Jaesung Kwon. 2021-08-12. Bianchi modular symbols and $p$-adic $L$-functions. https://doi.org/10.1016/j.jnt.2023.02.009

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