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 -adic Hecke -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 -adic measures. As an application, we extend the Ferrero-Greenberg formula of derivatives of -adic -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