Order of zeros of Dedekind zeta functions
Copyright policy )Order of zeros of Dedekind zeta functions
Answering a question of Browkin, we provide a new unconditional proof that the Dedekind zeta function of a number field L L has infinitely many nontrivial zeros of multiplicity at least 2 if L L has a subfield K K for which L / K L/K is a nonabelian Galois extension. We also extend this to zeros of order 3 when G a l ( L / K ) Gal(L/K) has an irreducible representation of degree at least 3, as predicted by the Artin holomorphy conjecture.
- College of New Jersey United States
- California Institute of Technology United States
- University of California, Los Angeles United States
- Massachusetts Institute of Technology United States
- University of Virginia Main Campus United States
Ordinary representations and characters, Artin \(L\)-functions, Dedekind zeta functions, Mathematics - Number Theory, Applied Mathematics, General Mathematics, 510, FOS: Mathematics, 11R42 (Primary) 20C15 (Secondary), grand simplicity hypothesis, Zeta functions and \(L\)-functions of number fields, Number Theory (math.NT)
Ordinary representations and characters, Artin \(L\)-functions, Dedekind zeta functions, Mathematics - Number Theory, Applied Mathematics, General Mathematics, 510, FOS: Mathematics, 11R42 (Primary) 20C15 (Secondary), grand simplicity hypothesis, Zeta functions and \(L\)-functions of number fields, Number Theory (math.NT)
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!