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• W3217209214 startingPage "978" @default.
• W3217209214 abstract "Let f be an algebraic valued periodic arithmetical function and L(s,f), defined as L(s,f):=∑n=1∞f(n)/ns for ℜ(s)>1, be the associated Dirichlet series. In this paper, we study the vanishing and arithmetic nature of the special values L(k,f) when k>1 is a positive integer. We prove a generalization of the Baker-Birch-Wirsing theorem conditional on the Polylog conjecture. Adopting a new approach, we define an induction operator on the space of periodic arithmetic functions, which makes precise the notion of an “imprimitive” arithmetic function. This enables us to obtain an analog of Okada's criterion for L(1,f)=0 and derive a natural decomposition of the vector spaceOk(N)={f:Z→Q|f(n+N)=f(n) for all n∈Z,L(k,f)=0}." @default.
• W3217209214 created "2021-12-06" @default.
• W3217209214 creator A5036760393 @default.
• W3217209214 creator A5069712392 @default.
• W3217209214 date "2022-09-01" @default.
• W3217209214 modified "2023-10-06" @default.
• W3217209214 title "On special values of Dirichlet series with periodic coefficients" @default.
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• W3217209214 doi "https://doi.org/10.1016/j.jnt.2021.10.011" @default.
• W3217209214 hasPublicationYear "2022" @default.
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