Journal of Advances in Mathematics and Computer Science

The Representations by Certain Duodenary Quadratic Forms

Bars Kendirli *

İstanbul Aydn University, Turkey.

*Author to whom correspondence should be addressed.

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Abstract

The determination of the number of representations of a positive integer by certain quadratic forms is an important goal of number theory. Formulae for N(1²ⁱ, 2^2j, 3^2k, 6^2l; n) for the nine octonary quadratic forms appear in the literature, whose coefficients are 1, 2, 3 and 6. Here, we determine formulae, for the numbers of representations of a positive integer by one hundred and six different duodenary quadratic forms whose coefficients are 1, 2, 3 and 6.

Keywords: Duodenary quadratic forms, representations, theta functions, Dedekind eta function, Eisenstein series, Eisenstein forms, modular forms, cusp forms.

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