REPRESENTATION OF NUMBERS BY SUMS OF SQUARES AND THE FORMS OF TYPE X2 1 + X1X2 + X2 2

摘要

In this paper, motivated from the work of Xia and Yao who obtained representation numbers of some octonary quadratic forms using theta function identities, we obtain representation numbers of certain quadratic forms in twelve variables with coecients 1, 2 and 4 which are sums of squares and the forms of type x2 1+x1x2+x2 2. The method of the proof is due to the authors Alaca, Alaca and Williams. Firstly, we establish some new theta function identities using the (p, k)-parametrization of theta functions and Eisenstein series given by Alaca, Alaca and Williams, and then use them to obtain the mentioned formulae.