Ramanujan’s theta functions and sums of triangular numbers

Zhi-Hong Sun

Type: Article

Publication Date: 2018-11-28

Citations: 10

DOI: https://doi.org/10.1142/s1793042119500520

Abstract

Let [Formula: see text] and [Formula: see text] be the set of integers and the set of positive integers, respectively. For [Formula: see text] let [Formula: see text] be the number of representations of [Formula: see text] by [Formula: see text], and let [Formula: see text] be the number of representations of [Formula: see text] by [Formula: see text] [Formula: see text]. In this paper, by using Ramanujan’s theta functions [Formula: see text] and [Formula: see text] we reveal some general relations between [Formula: see text] and [Formula: see text].

Locations

International Journal of Number Theory - View
arXiv (Cornell University) - View - PDF

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