Certain quaternary quadratic forms of level 48 and their representation numbers
B. Ramakrishnan, Brundaban Sahu, Anup Kumar Singh

TL;DR
This paper develops formulas for counting representations of integers by specific quaternary quadratic forms using modular forms of weight 2 on (48), advancing understanding of quadratic form representations.
Contribution
It constructs a basis for modular forms on (48) and derives explicit formulas for representation numbers of certain quadratic forms.
Findings
Formulas for representation numbers of specific quadratic forms derived.
Basis for modular forms on (48) established.
Enhanced methods for counting quadratic form representations.
Abstract
In this paper, we find a basis for the space of modular forms of weight on . We use this basis to find formulas for the number of representations of a positive integer by certain quaternary quadratic forms of the form , and , where 's belong to and 's belong to .
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Advanced Algebra and Geometry
