Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume -, Issue -, Pages -Publisher
AMER MATHEMATICAL SOC
DOI: 10.1000/proc/16041
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Funding
- National Science Foundation [DMS 2002265, DMS 205118]
- National Security Agency [H98230-21-1-0059]
- Thomas Jefferson Fund at the University of Virginia
- Templeton World Charity Foundation
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In this paper, 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 that is a nonabelian Galois extension. Moreover, we extend this result to zeros of order 3 when the Galois group Gal(L/K) has an irreducible representation of degree at least 3, as predicted by the Artin holomorphy conjecture.
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.
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