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- W2103995412 abstract "For any periodic function f:N→C with period q, we study the Dirichlet series L(s,f):=∑n≥1f(n)/ns. It is well-known that this admits an analytic continuation to the entire complex plane except at s=1, where it has a simple pole with residueρ:=q−1∑1≤a≤qf(a). Thus, the function is analytic at s=1 when ρ=0 and in this case, we study its non-vanishing using the theory of linear forms in logarithms and Dirichlet L-series. In this way, we give new proofs of an old criterion of Okada for the non-vanishing of L(1,f) as well as a classical theorem of Baker, Birch and Wirsing. We also give some new necessary and sufficient conditions for the non-vanishing of L(1,f)." @default.
- W2103995412 created "2016-06-24" @default.
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- W2103995412 date "2014-12-01" @default.
- W2103995412 modified "2023-10-18" @default.
- W2103995412 title "Non-vanishing of Dirichlet series with periodic coefficients" @default.
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- W2103995412 doi "https://doi.org/10.1016/j.jnt.2014.05.010" @default.
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