TY - JOUR
T1 - Weighted divisor sums and Bessel function series
AU - Berndt, Bruce C.
AU - Zaharescu, Alexandru
PY - 2006/6
Y1 - 2006/6
N2 - 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.
AB - 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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U2 - 10.1007/s00208-005-0734-3
DO - 10.1007/s00208-005-0734-3
M3 - Article
AN - SCOPUS:33646193277
SN - 0025-5831
VL - 335
SP - 249
EP - 283
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 2
ER -