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Generalized theta-functions with characteristics and cusp forms corresponding to quadratic forms in nine variables. (English) Zbl 1298.11036

Using modular properties of generalized theta-functions with characteristics the author constructs a cusp form of weight \({q\over 2}\) on the congruence subgroup \(\Gamma_0(48)\), which can be used to obtain exact formulas for the number of representations of positive integers by certain positive definite quadratic forms in nine variables.

MSC:

11F27 Theta series; Weil representation; theta correspondences
11E20 General ternary and quaternary quadratic forms; forms of more than two variables
11E25 Sums of squares and representations by other particular quadratic forms
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