English

Sum expressions for $p$-adic Hecke $L$-functions of totally real fields

Number Theory 2023-03-01 v2

Abstract

As a continuation of previous work, we establish sum expressions for pp-adic Hecke LL-functions of totally real fields in the sense of Delbourgo, assuming a totally real analog of Heegner hypothesis. This is done by finding explicit formulas of the periods of the corresponding pp-adic measures. As an application, we extend the Ferrero-Greenberg formula of derivatives of pp-adic LL-functions to this setting.

Keywords

Cite

@article{arxiv.2204.07364,
  title  = {Sum expressions for $p$-adic Hecke $L$-functions of totally real fields},
  author = {Luochen Zhao},
  journal= {arXiv preprint arXiv:2204.07364},
  year   = {2023}
}

Comments

Revised version with a new Appendix B and slightly strengthened/corrected results; to appear in Pure and Applied Mathematics Quarterly