Bull. Korean Math. Soc. 2013; 50(1): 241-261
Printed January 31, 2013
https://doi.org/10.4134/BKMS.2013.50.1.241
Copyright © The Korean Mathematical Society.
Daeyeoul Kim, Aeran Kim, and Hwasin Park
National Institute for Mathematical Sciences, Chonbuk National University, Chonbuk National University
In this paper, we find the coefficients for the Weierstrass $\wp(x)$ and $\wp''(x)(x= \frac{1}{2},\frac{\tau}{2}, \frac{\tau+1}{2})$-functions in terms of the arithmetic identities appearing in divisor functions which are proved by Ramanujan (\cite{S. Ram}). Finally, we reprove congruences for the functions $\mu(n)$ and $\nu(n)$ in Hahn's article \cite[Theorems 6.1 and 6.2]{Hahn}.
Keywords: Weierstrass $\wp(x)$ functions, convolution sums
MSC numbers: 11A67
2013; 50(4): 1389-1413
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd