Eisenstein series of \(3/2\) weight and one conjecture of Kaplansky
The paper studies the problem of how to find integers represented by a positive definite ternary quadratic form. Each of the forms determines a corresponding genus of forms. Following Kaplansky, any integer represented by some forms of the genus, is called an eligible number of the genus. The paper proves that the quadratic form \(f_{1}=x^2+y^2+7z^2\) represents all eligible numbers of the genus of \(f_{1}\) congruent to \(2 \bmod 3\) except \(14 \cdot 7^{2k}\). This result was conjectured by \textit{I. Kaplansky} [Math. Comput. 64, 341-345 (1995; Zbl 0826.11015)]. The present paper also studies some analogous problems for quadratic forms of special type from two class genera.
scientific article; zbMATH DE number 1782049