DIVISOR FUNCTION $\tau _{3} \left(\omega \right)$ WEIGHTED BY KLOOSTERMAN SUM
نویسندگان
چکیده
منابع مشابه
Weighted Divisor Sums and Bessel Function Series
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 positiv...
متن کاملDivisor-sum Fibers
Let s(·) denote the sum-of-proper-divisors function, that is, s(n) = ∑ d|n, d<n d. Erdős–Granville–Pomerance–Spiro conjectured that for any set A of asymptotic density zero, the preimage set s−1(A ) also has density zero. We prove a weak form of this conjecture: If (x) is any function tending to 0 as x→∞, and A is a set of integers of cardinality at most x 1 2 + , then the number of integers n ...
متن کاملWeighted Divisor Sums and Bessel Function Series, Ii
On page 335 in his lost notebook, Ramanujan recorded without proofs two identities involving finite trigonometric sums and doubly infinite series of Bessel functions. In each case, there are three possible interpretations for the double series. In an earlier paper, two of the present authors proved the first identity under one possible interpretation. In the present paper, the second identity i...
متن کاملWeighted Divisor Sums and Bessel Function Series, Iii
On page 335 in his lost notebook, Ramanujan recorded without proofs two identities involving finite trigonometric sums and doubly infinite series of Bessel functions. The two identities are intimately connected with the classical circle and divisor problems, respectively. For each of Ramanujan’s identities, there are three possible interpretations for the double series. In two earlier papers, t...
متن کاملcompactifications and function spaces on weighted semigruops
chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Journal of Pure and Apllied Mathematics
سال: 2014
ISSN: 1311-8080,1314-3395
DOI: 10.12732/ijpam.v89i5.9