Journal of the Ramanujan Mathematical Society

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The Deuring-Heilbronn Phenomenon for Artin L-functions


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1 Department of Mathematics, University of Toronto, 100 St. George Street, Toronto, Ontario, M5S 3G3, Canada
     

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Let E/K be a Galois extension of number fields with group G, and let x be a character of G. The goal of this note is to establish a version of the Deuring-Heilbronn Phenomenon (DHP) for non-Abelian Artin L-functions L(s,x,E/K) under the assumption of Artin's conjecture. The phenomenon, first observed for Dirichlet L-functions, is the fact that a zero of the L-function very close to s = 1 has the effect of pushing the other zeros away from the line σ = 1. In [1] a version of DHP for (K(S) has been proved. Here we generalize that result to non-Abelian L-functions.
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  • The Deuring-Heilbronn Phenomenon for Artin L-functions

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Authors

Kambiz Mahmoudian
Department of Mathematics, University of Toronto, 100 St. George Street, Toronto, Ontario, M5S 3G3, Canada

Abstract


Let E/K be a Galois extension of number fields with group G, and let x be a character of G. The goal of this note is to establish a version of the Deuring-Heilbronn Phenomenon (DHP) for non-Abelian Artin L-functions L(s,x,E/K) under the assumption of Artin's conjecture. The phenomenon, first observed for Dirichlet L-functions, is the fact that a zero of the L-function very close to s = 1 has the effect of pushing the other zeros away from the line σ = 1. In [1] a version of DHP for (K(S) has been proved. Here we generalize that result to non-Abelian L-functions.