A $p$-adic Stark conjecture in the rank one setting

Joseph Ferrara

A $p$-adic Stark conjecture in the rank one setting

Number Theory 2019-10-04 v2

Authors: Joseph Ferrara

Abstract

We give a new definition of a $p$ -adic $L$ -function for a mixed signature character of a real quadratic field and for a nontrivial ray class character of an imaginary quadratic field. We then state a $p$ -adic Stark conjecture for this $p$ -adic $L$ -function. We prove our conjecture in the case when $p$ is split in the imaginary quadratic field by relating our construction to Katz's $p$ -adic $L$ -function. We also provide numerical evidence for our conjecture in three examples.

Keywords

p-adic analysis p-adic hodge theory conjectures and proofs

Cite

@article{arxiv.1904.10561,
  title  = {A $p$-adic Stark conjecture in the rank one setting},
  author = {Joseph Ferrara},
  journal= {arXiv preprint arXiv:1904.10561},
  year   = {2019}
}

Comments

In Section 6 confirmed earlier calculations to higher precision and included more numerics in two of the examples. Made minor changes to fix typos

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