Results 261 to 270 of about 3,344 (284)

Evaluation of some convolution sums

AIP Conference Proceedings, 2015
We evaluate the convolution sums∑l+50m=nσ(l)σ(m), ∑2l+25m=nσ(l)σ(m), ∑l+25m=nσ(l)σ(m),∑l+m=n,l≡a mod⁡5σ(l)σ(m), for a=0,1,2,3,4using the theory of quasimodular forms.
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Higher convolutions of Ramanujan sums

Journal of Number Theory
Letting \(c_q(n)\) to be the Ramanujan sum, in the paper under review, the authors provide higher convolutions of Ramanujan sums by computing the following limit \[ \lim_{x\to x}\frac{1}{x}\sum_{n\leq x}c_{q_1}(n+a_1)\cdots c_{q_k}(n+a_k). \] The result of the above limit is a multivariable multiplicative function, say \(f(q_1,\dots, q_k)\), for which ...
Goel, Shivani, Murty, M. Ram
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Evaluate the Convolution Integral and Convolution Sum Use Compact Formula

2011 7th International Conference on Wireless Communications, Networking and Mobile Computing, 2011
Abstract: Convolution integral and convolution summation play an important role in the analysis of the linear time invariant systems. At present, many text books have published in my home country or foreign country , especially the ?sSignals and Systems?t all discuss the methods by use of the graph to determine the up limit, low limit and the interval ...
Bin Ren, De-yong Yu
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On convoluted sums

Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, 2016
Jean-Marie De Koninck, Imre Kátai
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Convolution Integral and Sum

2023
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Discrete Convolution Sum

2021
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The Convolution Sum

British Journal of Mathematics & Computer Science, 2014
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The multinomial convolution sums of certain divisor functions

Journal of Mathematical Analysis and Applications, 2017
Bumkyu Cho
exaly  

Shifted convolution sums for higher rank groups

Forum Mathematicum, 2019
Yujiao Jiang, Guangshi Lu
exaly  

CERTAIN COMBINATORIC CONVOLUTION SUMS AND THEIR RELATIONS TO BERNOULLI AND EULER POLYNOMIALS

Journal of the Korean Mathematical Society, 2015
Daeyeoul Kim, Abdelmejid Bayad
exaly