Vepkhvadze, Teimuraz Generalized theta-functions with characteristics and cusp forms corresponding to quadratic forms in nine variables. (English) Zbl 1298.11036 Bull. Georgian Natl. Acad. Sci. (N.S.) 5, No. 2, 25-30 (2011). 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. Reviewer: Meinhard Peters (Münster) 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 Keywords:modular forms; cusp forms; theta-function with characteristics; positive definite quadratic forms PDFBibTeX XMLCite \textit{T. Vepkhvadze}, Bull. Georgian Natl. Acad. Sci. (N.S.) 5, No. 2, 25--30 (2011; Zbl 1298.11036)