Representation numbers of seven quaternary quadratic forms each in a genus consisting of only two classes

Authors

AYŞE ALACA
ŞABAN ALACA
KENNETH WILLIAMS

DOI

10.3906/mat-1910-99

Abstract

The purpose of this paper is to present some examples of positive-definite integral nondiagonal quaternary quadratic forms whose representation numbers can be determined explicitly using the theory of modular forms. Very few such examples appear in the literature. The seven forms presented were selected because they each belong to a genus containing exactly two form classes for which the single genus mate is a diagonal form whose representation number has been determined recently.

Keywords

Representaion number, genus of quaternary quadratic forms, Dedekind eta function, eta quotients, theta functions, modular forms

First Page

1955

Last Page

1981

Recommended Citation

ALACA, AYŞE; ALACA, ŞABAN; and WILLIAMS, KENNETH (2020) "Representation numbers of seven quaternary quadratic forms each in a genus consisting of only two classes," Turkish Journal of Mathematics: Vol. 44: No. 6, Article 1. https://doi.org/10.3906/mat-1910-99
Available at: https://journals.tubitak.gov.tr/math/vol44/iss6/1