On the number of representations of certain quadratic forms and a formula for the Ramanujan Tau function
| Autor: | Ramakrishnan, B., Sahu, Brundaban, Singh, Anup Kumar |
|---|---|
| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we find the number of representations of the quadratic form $x_1^2+ x_1x_2 + x_2^2 + \ldots + x_{2k-1}^2 + x_{2k-1}x_{2k} + x_{2k}^2,$ for $k=7,9,11,12,14$ using the theory of modular forms. By comparing our formulas with the formulas obtained by G. A. Lomadze, we obtain the Fourier coefficients of certain newforms of level $3$ and weights $7,9,11$ in terms of certain finite sums involving the solutions of similar quadratic forms of lower variables. In the case of $24$ variables, comparison of these formulas gives rise to a new formula for the Ramanujan Tau function. Comment: 11 pages, minor revision, certain terms are combined to simplify formulas in Theorem 2.3 |
| Databáze: | arXiv |
| Externí odkaz: |
|