Results 241 to 250 of about 52,800 (268)

On Convoluted Numbers and Sums

The American Mathematical Monthly, 1967
(1967). On Convoluted Numbers and Sums. The American Mathematical Monthly: Vol. 74, No. 3, pp. 235-246.
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Sums with convolutions of Dirichlet characters

manuscripta mathematica, 2010
Let \(\chi_1\) and \(\chi_2\) be primitive Dirichlet characters with conductors \(q_1\) and \(q_2\), respectively, and let \[ S_{\chi_1,\chi_2}(X):=\sum_{ab\leq X}\chi_1(a)\chi_2(b). \] The authors prove that if \(X\geq q_2^{\frac 23}\geq q_1^{\frac 23}\) and \(\log X=q_2^{o(1)}\), then \[ \left| S_{\chi_1,\chi_2}(X)\right|\leq X^{\frac {13}{18}}q_1 ...
Banks, William D., Shparlinski, Igor E.
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The convolution sums of MacMahon’s q-series

The Ramanujan Journal
In his classical work on partitions and divisor functions, MacMahon introduced the two \(q\)-series \(A_k(q)\) and \(C_k(q)\), which have since been shown to be quasimodular forms and are closely linked to partition functions, modular forms, and infinite product identities.
Xia, Ernest X. W., Fan, Yan, Yao, Olivia X. M.   +2 more
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CONVOLUTIONS OF RAMANUJAN SUMS AND INTEGRAL CIRCULANT GRAPHS

International Journal of Number Theory, 2012
There exist several generalizations of the classical Dirichlet convolution, for instance the so-called A-convolutions analyzed by Narkiewicz. We shall connect the concept of A-convolutions satisfying a weak form of regularity and Ramanujan sums with the spectrum of integral circulant graphs.
Le, T. A., Sander, J. W.
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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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Convolution sums of restricted divisor functions derived from Dirichlet convolution

Publicationes Mathematicae Debrecen
In this article, the convolution sums of six restricted divisor functions considered by Glaisher are studied. Using the properties of Dirichlet convolution, we try to find the inverse functions of four restricted divisor functions and use these to find the formulae for the convolution sums under the given relatively primeness conditions.
Su Yeon Kong, Yan Li, Daeyeoul Kim
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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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Bounds on shifted convolution sums for Hecke eigenforms

Research in Number Theory, 2022
Asbjørn Christian Nordentoft, Morten S Risager   +1 more
exaly  

Discrete Convolution Sum

2021
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Convolution Integral and Sum

2023
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