Pure and Applied Mathematics Quarterly
Volume 19 (2023)
Sum expressions for $p$-adic Hecke $L$-functions of totally real fields
Pages: 597 – 639
As a continuation of previous work, we establish sum expressions for $p$-adic Hecke $L$-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 $p$-adic measures. As an application, we extend the Ferrero–Greenberg formula of derivatives of $p$-adic $L$-functions to this setting.
infinite sum, totally real $p$-adic Hecke $L$-functions, Ferrero–Greenberg derivative formula, Brumer–Stark unit, Iwasawa invariants
2010 Mathematics Subject Classification
Primary 11S40. Secondary 11S80, 11Y35.
Received 31 July 2022
Received revised 15 February 2023
Accepted 27 February 2023
Published 7 April 2023