For each real-valued nonprincipal character x mod k, letA(n) = x(d) and F(x) = Σ:dn* Prove thatF(x) = L(1,x) log x + O(1).n

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Answered: For each real-valued nonprincipal…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.4: Logarithmic Functions

Problem 37E

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For each real-valued nonprincipal character x mod k, let A(n) = x(d) and F(x) = Σ : dn * Prove that F(x) = L(1,x) log x + O(1). n