Journal of the Ramanujan Mathematical Society

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Zeros of Dedekind Zeta Functions and Holomorphy of Artin L-Functions


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1 Department of Mathematics, Queen’s University, Kingston, Ontario K7L 3N6, Canada
     

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For any Galois extension K/k of number fields, we show that every Artin L-function for Gal(K/k) is holomorphic at s = s0 ≠= 1 whenever the quotient ζK (s)/ζk (s) of Dedekind zeta functions has a zero of order at most max{2, p2 − 2} at s = s0 (here p2 stands for the second smallest prime divisor of [K : k]). This result gives a refinement of the previous work of Foote and V. K. Murty.
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  • Zeros of Dedekind Zeta Functions and Holomorphy of Artin L-Functions

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Authors

Peng-Jie Wong
Department of Mathematics, Queen’s University, Kingston, Ontario K7L 3N6, Canada

Abstract


For any Galois extension K/k of number fields, we show that every Artin L-function for Gal(K/k) is holomorphic at s = s0 ≠= 1 whenever the quotient ζK (s)/ζk (s) of Dedekind zeta functions has a zero of order at most max{2, p2 − 2} at s = s0 (here p2 stands for the second smallest prime divisor of [K : k]). This result gives a refinement of the previous work of Foote and V. K. Murty.

References