Order of zeros of Dedekind zeta functions

Hu, Daniel and Kaneko, Ikuya and Martin, Spencer and Schildkraut, Carl (2022) Order of zeros of Dedekind zeta functions. Proceedings of the American Mathematical Society, 150 (12). pp. 5111-5120. ISSN 0002-9939. doi:10.1090/proc/16041. https://resolver.caltech.edu/CaltechAUTHORS:20220707-977591000

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Abstract

Answering a question of Browkin, we provide a new unconditional proof that the Dedekind zeta function of a number field L has infinitely many nontrivial zeros of multiplicity at least 2 if L has a subfield K for which L/K is a nonabelian Galois extension. We also extend this to zeros of order 3 when Gal(L/K) has an irreducible representation of degree at least 3, as predicted by the Artin holomorphy conjecture.

Item Type:

Article

Related URLs:

URL	URL Type	Description
https://doi.org/10.1090/proc/16041	DOI	Article
https://arxiv.org/abs/2107.03269	arXiv	Discussion Paper

ORCID:

Author	ORCID
Kaneko, Ikuya	0000-0003-4518-1805

Additional Information:

© 2022 American Mathematical Society. Received by editor(s): July 22, 2021. Received by editor(s) in revised form: February 10, 2022. Published electronically: June 17, 2022. The authors were supported by the National Science Foundation (Grants DMS 2002265 and DMS 205118), National Security Agency (Grant H98230-21-1-0059), the Thomas Jefferson Fund at the University of Virginia, and the Templeton World Charity Foundation. We are deeply grateful to Peter Humphries for supervising this project and to Ken Ono for his valuable suggestions. We would also like to thank Robert Lemke Oliver and Samit Dasgupta for helpfully directing us to the work of Stark.

Funders:

Funding Agency	Grant Number
NSF	DMS-2002265
NSF	DMS-205118
National Security Agency	H98230-21-1-0059
University of Virginia	UNSPECIFIED
Templeton World Charity Foundation	UNSPECIFIED

Issue or Number:

Classification Code:

MSC (2020): Primary 11R42; Secondary 20C15

DOI:

10.1090/proc/16041

Record Number:

CaltechAUTHORS:20220707-977591000

Persistent URL:

https://resolver.caltech.edu/CaltechAUTHORS:20220707-977591000

Usage Policy:

No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

115417

Collection:

CaltechAUTHORS

Deposited By:

George Porter

Deposited On:

12 Jul 2022 15:11

Last Modified:

31 Jan 2023 23:15

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