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On extended interpolation properties of the Katz p-adic L-function
Abstract
We describe extended interpolation properties of the Katz p-adic L-function over an imaginary quadratic field. We have three applications. Firstly, we give an elliptic analogue of the Coleman-Ihara formula. Secondly, we extend Kato's explicit reciprocity law for elliptic units and give a proof of the Tamagawa number conjecture for critical Hecke motives. Finally, we prove a large part of the p-adic Beilinson conjecture for the Katz p-adic L-function.
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BibTeX
@misc{sano2026extended,
title = {{On extended interpolation properties of the Katz $p$-adic $L$-function}},
author = {Takamichi Sano and Otmar Venjakob},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36607},
eprint = {2610.36607},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36607},
}
RIS
TY - UNPB
TI - On extended interpolation properties of the Katz p-adic L-function
AU - Takamichi Sano
AU - Otmar Venjakob
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.36607
UR - https://arxiv.org/abs/2610.36607
AB - We describe extended interpolation properties of the Katz p-adic L-function over an imaginary quadratic field. We have three applications. Firstly, we give an elliptic analogue of the Coleman-Ihara formula. Secondly, we extend Kato's explicit reciprocity law for elliptic units and give a proof of the Tamagawa number conjecture for critical Hecke motives. Finally, we prove a large part of the p-adic Beilinson conjecture for the Katz p-adic L-function.
ER -