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

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

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)
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