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Relevant bibliographies by topics / Ramanujan sums

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Journal articles

Academic literature on the topic 'Ramanujan sums'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Ramanujan sums"

1

Chan, T. H., and A. V. Kumchev. "On sums of Ramanujan sums." Acta Arithmetica 152, no. 1 (2012): 1–10. http://dx.doi.org/10.4064/aa152-1-1.

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2

Laohakosol, Vichian, Pattira Ruengsinsub, and Nittiya Pabhapote. "Ramanujan sums via generalized Möbius functions and applications." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–34. http://dx.doi.org/10.1155/ijmms/2006/60528.

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A generalized Ramanujan sum (GRS) is defined by replacing the usual Möbius function in the classical Ramanujan sum with the Souriau-Hsu-Möbius function. After collecting basic properties of a GRS, mostly containing existing ones, seven aspects of a GRS are studied. The first shows that the unique representation of even functions with respect to GRSs is possible. The second is a derivation of the mean value of a GRS. The third establishes analogues of the remarkable Ramanujan's formulae connecting divisor functions with Ramanujan sums. The fourth gives a formula for the inverse of a GRS. The fi

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3

Fujisawa, Yusuke. "On sums of generalized Ramanujan sums." Indian Journal of Pure and Applied Mathematics 46, no. 1 (2015): 1–10. http://dx.doi.org/10.1007/s13226-015-0103-1.

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4

Tóth, László. "Sums of products of Ramanujan sums." ANNALI DELL'UNIVERSITA' DI FERRARA 58, no. 1 (2011): 183–97. http://dx.doi.org/10.1007/s11565-011-0143-3.

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5

Fowler, Christopher F., Stephan Ramon Garcia, and Gizem Karaali. "Ramanujan sums as supercharacters." Ramanujan Journal 35, no. 2 (2013): 205–41. http://dx.doi.org/10.1007/s11139-013-9478-y.

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6

Kiuchi, Isao. "Sums of averages of generalized Ramanujan sums." Journal of Number Theory 180 (November 2017): 310–48. http://dx.doi.org/10.1016/j.jnt.2017.03.026.

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7

KIUCHI, Isao. "On Sums of Averages of Generalized Ramanujan Sums." Tokyo Journal of Mathematics 40, no. 1 (2017): 255–75. http://dx.doi.org/10.3836/tjm/1502179227.

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8

Chen, Guangyi, Sridhar Krishnan, and Tien D. Bui. "Matrix-Based Ramanujan-Sums Transforms." IEEE Signal Processing Letters 20, no. 10 (2013): 941–44. http://dx.doi.org/10.1109/lsp.2013.2273973.

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9

BERNDT, BRUCE C., and PING XU. "An Integral Analogue of Theta Functions and Gauss Sums in Ramanujan's Lost Notebook." Mathematical Proceedings of the Cambridge Philosophical Society 147, no. 2 (2009): 257–65. http://dx.doi.org/10.1017/s0305004109002552.

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AbstractOne page in Ramanujan's lost notebook is devoted to claims about a certain integral with two parameters. One claim gives an inversion formula for the integral that is similar to the transformation formula for theta functions. Other claims are remindful of Gauss sums. In this paper we prove all the claims made by Ramanujan about this integral.

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10

Cooper, Shaun, and Michael Hirschhorn. "Sums of Squares and Sums of Triangular Numbers." gmj 13, no. 4 (2006): 675–86. http://dx.doi.org/10.1515/gmj.2006.675.

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Abstract Motivated by two results of Ramanujan, we give a family of 15 results and 4 related ones. Several have interesting interpretations in terms of the number of representations of an integer by a quadratic form , where λ1 + . . . + λ𝑚 = 2, 4 or 8. We also give a new and simple combinatorial proof of the modular equation of order seven.

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