Bernoulli Identities and Combinatoric Convolution Sums with Odd Divisor Functions
Abstract and Applied Analysis, 2014 We study the combinatoric convolution sums involving odd divisor functions, their relations to Bernoulli numbers, and some interesting applications.
Daeyeoul Kim, Yoon Kyung Park
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Bernoulli numbers, convolution sums and congruences of coefficients for certain generating functions [PDF]
, 2013 In this paper, we study the convolution sums involving restricted divisor functions, their generalizations, their relations to Bernoulli numbers, and some interesting applications.MSC: 11B68, 11A25, 11A67, 11Y70, 33E99.
Daeyeoul Kim +2 more
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EVALUATING CONVOLUTION SUMS OF THE DIVISOR FUNCTION BY QUASIMODULAR FORMS [PDF]
International Journal of Number Theory, 2007 We provide a systematic method to compute arithmetic sums including some previously computed by Alaca, Besge, Cheng, Glaisher, Huard, Lahiri, Lemire, Melfi, Ou, Ramanujan, Spearman and Williams. Our method is based on quasimodular forms. This extension of modular forms has been constructed by Kaneko and Zagier.
Emmanuel Royer
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On asymptotics of shifted sums of Dirichlet convolutions
, 2023 26 pages.
Jiseong Kim
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Shifted convolution sums motivated by string theory
Journal of Number Theory, 2023 In \cite{CGPWW2021}, it was conjectured that a particular shifted sum of even divisor sums vanishes, and in \cite{SDK}, a formal argument was given for this vanishing. Shifted convolution sums of this form appear when computing the Fourier expansion of coefficients for the low energy scattering amplitudes in type IIB string theory \cite{GMV2015} and ...
Kim Klinger-Logan, Ksenia Fedosova
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CONVOLUTION SUMS AND THEIR RELATIONS TO EISENSTEIN SERIES [PDF]
Bulletin of the Korean Mathematical Society, 2013 In this paper, we consider several convolution sums, namely, Ai(m;n; N) (i = 1; 2; 3; 4), Bj(m;n;N) (j = 1; 2; 3), and Ck(m;n;N) (k = 1; 2; 3;:::, 12), and establish certain identities involving their nite products. Then we extend these types of product convolution identities to products involving Faulhaber sums.
Daeyeoul Kim +2 more
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Euler Polynomials and Combinatoric Convolution Sums of Divisor Functions with Even Indices
Abstract and Applied Analysis, 2014 We study combinatoric convolution sums of certain divisor functions involving even indices. We express them as a linear combination of divisor functions and Euler polynomials and obtain identities D2k(n)=(1/4)σ2k+1,0(n;2)-2·42kσ2k+1(n/4) -(1/2)[∑d|n,d ...
Daeyeoul Kim +2 more
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Convergence of Sums to a Convolution of Stable Laws [PDF]
The Annals of Mathematical Statistics, 1970 J. David Mason
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Binomial convolution sum of divisor functions associated with Dirichlet character modulo 8
Open MathematicsIn this article, we compute binomial convolution sums of divisor functions associated with the Dirichlet character modulo 8, which is the remaining primitive Dirichlet character modulo powers of 2 yet to be considered.
Jin Seokho, Park Ho
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Certain combinatoric Bernoulli polynomials and convolution sums of divisor functions [PDF]
, 2013 It is known that certain convolution sums can be expressed as a combination of divisor functions and Bernoulli formula. One of the main goals in this paper is to establish combinatoric convolution sums for the divisor sums σˆs(n)=∑d|n(−1)nd−1ds. Finally,
Daeyeoul Kim +1 more
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