Identities involving the coefficients of a class of Dirichlet series. VII

Bruce C. Berndt
1975 Transactions of the American Mathematical Society  
Let a(n) be an arithmetical function, and consider the Riesz sum Ap(x) = £n<x a(n)(x ~ n)p-F°r a(") belonging to a certain class of arithmetical functions, Ap(x) can be expressed in terms of an infinite series of Bessel functions. K. Chandrasekharan and R. Narasimhan have established this identity for the widest known range of p. Their proof depends upon equi-convergence theory of trigonometric series. An alternate proof is given here which uses only the classical theory of Bessel functions.
doi:10.1090/s0002-9947-1975-0352018-5 fatcat:xcttpjuxfffzjklw3cryviaa7a