Weighted Divisor Sums and Bessel Function Series | Zendy

Bruce C. Berndt | Zendy; Alexandru Zaharescu | Zendy

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Weighted Divisor Sums and Bessel Function Series

Author(s) -

Bruce C. Berndt,

Alexandru Zaharescu

Publication year - 2006

Publication title -

mathematische annalen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.235

H-Index - 75

eISSN - 1432-1807

pISSN - 0025-5831

DOI - 10.1007/s00208-005-0734-3

Subject(s) - mathematics , bessel function , divisor function , ramanujan's sum , identity (music) , series (stratigraphy) , combinatorics , integer (computer science) , divisor (algebraic geometry) , generating function , function (biology) , number theory , binomial coefficient , discrete mathematics , algebra over a field , pure mathematics , mathematical analysis , physics , computer science , acoustics , programming language , paleontology , evolutionary biology , biology

On page 335 in his lost notebook, Ramanujan records without proof an identity involving a finite trigonometric sum and a doubly infinite series of ordinary Bessel functions. We provide the first published proof of this result. The identity yields as corollaries representations of weighted divisor sums, in particular, the summatory function for r2(n), the number of representations of the positive integer n as a sum of two squares.

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