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Some Generalizations of Ramanujan's Sum [PDF]
Canadian Journal of Mathematics, 1980 Ramanujan's well known trigonometrical sum C(m, n) denned bywhere x runs through a reduced residue system (mod n), had been shown to occur in analytic problems concerning modular functions of one variable, by Poincaré [4]. Ramanujan, independently later, used these trigonometrical sums in his remarkable work on representation of integers as sums of ...
K. G. Ramanathan, M. Venkata Subbarao
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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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Some Special Integer Partitions Generated by a Family of Functions
Trends in Computational and Applied Mathematics, 2023 In this work, inspired by Ramanujan’s fifth order Mock Theta function f1(q), we define a collection of functions and look at them as generating functions for partitions of some integer n containing at least m parts equal to each one of the numbers from
M. L. Matte
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Legendre Ramanujan Sums transform [PDF]
2015 23rd European Signal Processing Conference (EUSIPCO), 2015 Publication in the conference proceedings of EUSIPCO, Nice, France ...
Pei, Soo-Chang, Wen, Chia Chang
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A domain free of the zeros of the partial theta function
Математичні Студії, 2023 The partial theta function is the sum of the series \medskip\centerline{$\displaystyle\theta (q,x):=\sum\nolimits _{j=0}^{\infty}q^{j(j+1)/2}x^j$,} \medskip\noi where $q$ is a real or complex parameter ($|q|
V. Kostov
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Infinite Product Representation for the Szegö Kernel for an Annulus
Journal of Function Spaces, 2022 The Szegö kernel has many applications to problems in conformal mapping and satisfies the Kerzman-Stein integral equation. The Szegö kernel for an annulus can be expressed as a bilateral series and has a unique zero.
Nuraddeen S. Gafai +2 more
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Ramanujan sums as supercharacters [PDF]
The Ramanujan Journal, 2013 The theory of supercharacters, recently developed by Diaconis-Isaacs and Andre, can be used to derive the fundamental algebraic properties of Ramanujan sums. This machinery frequently yields one-line proofs of difficult identities and provides many novel formulas.
Fowler, Christopher F. +2 more
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ALMOST A CENTURY OF ANSWERING THE QUESTION: WHAT IS A MOCK THETA FUNCTION? [PDF]
, 2014 Quite a few famous and extraordinarily gifted mathematicians led lives that were tragically cut short. Ramanujan is certainly among them. While suffering from a fatal disease, he discovered what he called mock theta functions.
W. Duke
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Multi-sum Rogers-Ramanujan type identities
Journal of Mathematical Analysis and Applications, 2023 We use an integral method to establish a number of Rogers-Ramanujan type identities involving double and triple sums. The key step for proving such identities is to find some infinite products whose integrals over suitable contours are still infinite products. The method used here is motivated by Rosengren's proof of the Kanade-Russell identities.
Zhineng Cao, Liuquan Wang
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