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Arithmetic properties derived from coefficients of certain eta quotients
- Source :
- Journal of Inequalities and Applications, Vol 2020, Iss 1, Pp 1-23 (2020)
- Publication Year :
- 2020
- Publisher :
- SpringerOpen, 2020.
-
Abstract
- Abstract For a positive integer k, let F ( q ) k : = ∏ n ≥ 1 ( 1 − q n ) 4 k ( 1 + q 2 n ) 2 k = ∑ n ≥ 0 a k ( n ) q n $$ F (q)^{k}:= \prod_{n \geq 1} \frac{(1-q^{n})^{4k}}{(1+q^{2n})^{2k}} = \sum_{n\geq 0} \frak{a}_{k} (n)q^{n} $$ be the eta quotients. The coefficients a 1 ( n ) $\frak{a}_{1} (n)$ can be interpreted as a certain kind of restricted divisor sums. In this paper, we give the signs and modulo values for a 1 ( n ) $\frak{a}_{1} (n)$ and a 2 ( m ) $\frak{a}_{2} (m)$ and calculate several convolution sums involving a k ( n ) $\frak{a}_{k} (n)$ .
Details
- Language :
- English
- ISSN :
- 1029242X
- Volume :
- 2020
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Journal of Inequalities and Applications
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.46f12dabd604c2eb2739df1960c0c23
- Document Type :
- article
- Full Text :
- https://doi.org/10.1186/s13660-020-02368-y