Results 11 to 20 of about 52,924 (309)
CONVOLUTION SUM OF RAMANUJAN'S SUM
, 2022 This article is the result of calculating the convolution of Ramanujan's sum and natural number multiplied. Among these results, special values are expressed by Euler and Bernoulli functions.
Gye Hwan Jo +2 more
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Deep Generalized Convolutional Sum-Product Networks [PDF]
, 2019 Sum-Product Networks (SPNs) are hierarchical, graphical models that combine benefits of deep learning and probabilistic modeling. SPNs offer unique advantages to applications demanding exact probabilistic inference over high-dimensional, noisy inputs. Yet, compared to convolutional neural nets, they struggle with capturing complex spatial relationships
Jos van de Wolfshaar, Andrzej Pronobis
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CONVOLUTION SUMS INVOLVING THE DIVISOR FUNCTION [PDF]
Proceedings of the Edinburgh Mathematical Society, 2004 AbstractThe series\begin{alignat*}{2} L_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \\ M_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma_3(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \\ N_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma_5(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \end{alignat*}are evaluated and used to prove convolution formulae such ...
Cheng, Nathalie, Williams, Kenneth S.
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Convolution identities for divisor sums and modular forms. [PDF]
Proc Natl Acad Sci U S AWe consider certain convolution sums that are the subject of a conjecture by Chester, Green, Pufu, Wang, and Wen in string theory. We prove a generalized form of their conjecture, explicitly evaluating absolutely convergent sums ∑
Fedosova K +2 more
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Bounds for the Rate of Convergence in the Generalized Rényi Theorem
Mathematics, 2022 In the paper, an overview is presented of the results on the convergence rate bounds in limit theorems concerning geometric random sums and their generalizations to mixed Poisson random sums, including the case where the mixing law is itself a mixed ...
Victor Korolev
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Iterated Binomial Sums and their Associated Iterated Integrals [PDF]
, 2014 We consider finite iterated generalized harmonic sums weighted by the binomial $\binom{2k}{k}$ in numerators and denominators. A large class of these functions emerges in the calculation of massive Feynman diagrams with local operator insertions starting
't Hooft G. +20 more
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General convolution sums involving Fibonacci m-step numbers [PDF]
In this paper, using a generating function approach, we derive several new convolution sum identities involving Fibonacci m-step numbers. As special instances of the results derived herein, we will get many new and known results involving Fibonacci, Tribonacci, Tetranacci and Pentanacci numbers.
Robert Frontczak, Karol Gryszka
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Factors of alternating convolution of the Gessel numbers [PDF]
Notes on Number Theory and Discrete MathematicsThe Gessel number P(n,r) is the number of lattice paths in the plane with (1,0) and (0,1) steps from (0,0) to (n+r, n+r-1) that never touch any of the points from the set {(x,x)∈ℤ²:x≥r}. We show that there is a close relationship between Gessel numbers P(
Jovan Mikić
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Arithmetic properties derived from coefficients of certain eta quotients
Journal of Inequalities and Applications, 2020 For a positive integer k, let F ( q ) k : = ∏ n ≥ 1 ( 1 − q n ) 4 k ( 1 + q 2 n ) 2 k = ∑ n ≥ 0 a k ( n ) q n $$ F (q)^{k}:= \prod_{n \geq 1} \frac{(1-q^{n})^{4k}}{(1+q^{2n})^{2k}} = \sum_{n\geq 0} \frak{a}_{k} (n)q^{n} $$ be the eta quotients.
Jihyun Hwang, Yan Li, Daeyeoul Kim
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