Abstract
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 r 2(n), the number of representations of the positive integer n as a sum of two squares.
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. J. London Math. Soc. (2) 4, 385–393 (1972)Author information
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Research partially supported by grant MDA H92830-04-1-0027 from the National Security Agency.
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Berndt, B., Zaharescu, A. Weighted Divisor Sums and Bessel Function Series. Math. Ann. 335, 249–283 (2006). https://doi.org/10.1007/s00208-005-0734-3
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DOI: https://doi.org/10.1007/s00208-005-0734-3