CONVOLUTION SUMS AND THEIR RELATIONS TO EISENSTEIN SERIES

Title & Authors
CONVOLUTION SUMS AND THEIR RELATIONS TO EISENSTEIN SERIES
Kim, Daeyeoul; Kim, Aeran; Sankaranarayanan, Ayyadurai;

Abstract
In this paper, we consider several convolution sums, namely, $\small{\mathcal{A}_i(m,n;N)}$ ($i Keywords sum of divisor functions;convolution sums;Faulhaber sums;Eisenstein series;elliptic function; Language English Cited by References 1. B. C. Berndt, Ramanujan's Notebooks. Part II, Springer-Verlag, New York, 1989. 2. B. C. Berndt and A. J. Yee, Congruences for the coecients of quotients of Eisenstein series, Acta Arith. 104 (2002), no. 3, 297-308. 3. J. W. L. Glaisher, On the square of the series in which the coecients are the sums of the divisors of the exponents, Mess. Math. 14 (1884), 156{163. 4. H. Hahn, Convolution sums of some functions on divisors, Rocky Mountain J. Math. 37 (2007), no. 5, 1593-1622. 5. J. G. Huard, Z. M. Ou, B. K. Spearman, and K. S. Williams, Elementary evaluation of certain convolution sums involving divisor functions, Number theory for the millennium, II (Urbana, IL, 2000), 229-274, A K Peters, Natick, MA, 2002. 6. D. Kim, A. Kim, and Y. Li, Convolution sums arising from the divisor functions, J. Korean Math. Soc. 50 (2013), no. 2, 331-360. 7. D. Kim, A. Kim, and H. Park, Congruences of the Weierstrass$\delta(x)$and${\delta}"(x)$(x =$\frac{1}{2}$,$\frac{\tau}{2}$,$\frac{{\tau}+1}{2}\$) - functions on divisors, Bull. Korean Math. Soc. 50 (2013), no. 1, 241-261.

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