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Journal of the Ramanujan Mathematical Society

Volume 34, Issue 2, June 2019  pp. 253–261.

Zeros of Dedekind zeta functions and holomorphy of Artin L-functions

Authors:  Peng-Jie Wong
Author institution:Department of Mathematics, Queen's University, Kingston, Ontario K7L 3N6, Canada

Summary:  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)/ζ k(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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