On the number of representations of integers by quadratic forms in twelve variables. (English) Zbl 0915.11023

Lomadze, G.

Georgian Math. J. 5, No. 6, 545-564 (1998).

Continuing earlier research, the author proves formulas for the number of representations of integers by the following quadratic forms \[ \begin{aligned} f_1 & = x^2_1+\cdots+ x^2_{10}+ 2(x^2_{11}+ x^2_{12}),\\ f_2 & = x^2_1+\cdots+ x^2_6+ 2(x^2_7+\cdots+ x^2_{12}),\\ f_3 & = x^2_1+ x^2_2+ 2(x^2_3+\cdots+ x^2_{12}),\\ f_4 & = x^2_1+\cdots +x^2_8+ 2(x^2_9+ x^2_{10})+ 4(x^2_{11}+ x^2_{12}).\end{aligned} \] {}.

Reviewer: M.Peters (Münster)

MSC:

11E20	General ternary and quaternary quadratic forms; forms of more than two variables
11E25	Sums of squares and representations by other particular quadratic forms
11F27	Theta series; Weil representation; theta correspondences
11E45	Analytic theory (Epstein zeta functions; relations with automorphic forms and functions)

Keywords:

modular forms; theta-functions; of integers; representations; quadratic forms