Identities involving the coefficients of a class of Dirichlet series. VII
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- by Bruce C. Berndt PDF
- Trans. Amer. Math. Soc. 201 (1975), 247-261 Request permission
Abstract:
Let $a(n)$ be an arithmetical function, and consider the Riesz sum ${A_\rho }(x) = {\Sigma _{n \leq x}}a(n){(x - n)^\rho }$. For $a(n)$ belonging to a certain class of arithmetical functions, ${A_\rho }(x)$ 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 $\rho$. 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.References
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Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 201 (1975), 247-261
- MSC: Primary 10H10; Secondary 30A16
- DOI: https://doi.org/10.1090/S0002-9947-1975-0352018-5
- MathSciNet review: 0352018