Representations by quaternary quadratic forms with coefficients 1, 2, 5 or 10

Ay\c{s}e Alaca; Mada Altiary

doi:10.4134/CKMS.c170468

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Commun. Korean Math. Soc. 2019; 34(1): 27-41

Online first article November 20, 2018 Printed January 31, 2019

https://doi.org/10.4134/CKMS.c170468

Representations by quaternary quadratic forms with coefficients 1, 2, 5 or 10

Ay\c{s}e Alaca, Mada Altiary

Carleton University; Carleton University

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Abstract

We determine explicit formulas for the number of representations of a positive integer $n$ by quaternary quadratic forms with coefficients $1$, $2$, $5$ or $10$. We use a modular forms approach.

Keywords: quaternary quadratic forms, representations, theta functions, Dedekind eta function, eta quotients, modular forms, Eisenstein forms, cusp forms

MSC numbers: 11E25, 11E20, 11F11, 11F20, 11F27