Few more relations connecting Ramanujan-type Eisenstein series and cubic theta functions of Borewein

키워드

참고문헌 (12)

1. A. PAlaca, "Evaluation of the convolution sums l+12m=n (l)(m) and P 3l+4m=n (l)(m)", Advances in Theoretical and Applied Math-ematics, 1(1), pp.27~48 (2006)
2. A. Alaca, "On the two dimensional theta functions of the Borweins", Acta Arithmetica, 124(2), pp.177~195 (2006)
3. A. PAlaca, "Evaluation of the convolution sums l+6m=n (l)(m)and P 2l+3m=n (l)(m)", Journal of Number Theory, 124(2), pp.491~510 (2007)
4. B. C. Berndt, "Ramanujan's Notebooks, Part III" (1991), Springer
5. B. C. Berndt, "Number Theory in the Spirit of Ramanujan" (2006), American mathematical Society
6. J. M. Borwein, "A cubic counterpart of Jacobi's identity and the AGM", Trans. Am. Math. Soc, 323, pp.691~701 (1991)
7. J. W. L. Glaisher, "On the square of the series in which the coeff's are the sum of the divisors of the exponents", Mess. Math., 14, pp.156~163 (1885)
8. S. Ramanujan, "Notebooks, Vols. 1,2" (1957), Tata Institute of Fundamental Research
9. H. C. Vidya, "Some studies on Eisenstein series and its applications", Notes on Number Theory and Discrete Mathematics, 25(4), pp.30~43 (2019)
10. Shruthi, "Srivatsa Kumar, Some new Eisenstein series containing the Borewein's cubic theta functions and convolution sum P i+4j=n (i)(j);", Afrika Math-ematika, 31, pp.971~982 (2020)
11. K. S. Williams, "The convolution sum P m<n=8(l)(n-8m)", Pacific Journal of Math-ematics, 228(2), pp.387~396 (2006)
12. E. X. W. Xia, "Eisenstein series identities involving the Borwein's cubic theta functions", Journal of Applied Mathematics, pp.181264~ (2012)

관련 논문AI추천