Results 281 to 290 of about 1,582,878 (315)

Shifted convolution sums related to Hecke–Maass forms

The Ramanujan Journal, 2020
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Tang, Hengcai, Wu, Jie
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Gas path parameter prediction of aero-engine based on an autoregressive discrete convolution sum process neural network

Chaos, Solitons & Fractals, 2021
Zhiquan Cui, Zhiqi Yan, Minghang Zhao, S. Zhong   +3 more
semanticscholar   +1 more source

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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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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Some new Eisenstein series containing the Borweins’ cubic theta functions and convolution sum $$\displaystyle {\sum _{i+4j=n}^{}\sigma (i)\sigma (j)}$$

, 2020
Shruthi, B. R. S. Kumar
semanticscholar   +1 more source

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
openaire   +1 more source