Geodesic
Eligible integers represented by positive ternary quadratic forms
Wei Lu 1   ; Hourong Qin 1
1 Department of Mathematics Nanjing University 210093 Nanjing, China
Acta Arithmetica, Tome 179 (2017) no. 1, pp. 17-23 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Assume that $f$ is a positive definite integral ternary quadratic form. Let $N_f$ denote the level of $f$. Assume that there are exactly two classes in gen$(f)$ and let $g$ be a representative of the other class. Assume further that $f$ and $g$ are in the same spinor genus. We show that if $M$ with $(M,N_f)=1$ is an eligible integer which is not square-free, then it can be represented by $f$. This generalizes Ono and Soundararajan’s 1997 result for $f=x_1^2+x_2^2+10x_3^2$, Wang and Pei’s 2001 result for $f=x_1^2+7x_2^2+7x_3^2$ and Kelley’s 2001 result for $f=x_1^2+x_2^2+7x_3^2$.
DOI : 10.4064/aa8498-2-2017
Keywords: assume positive definite integral ternary quadratic form denote level assume there exactly classes gen representative other class assume further spinor genus eligible integer which square free represented generalizes ono soundararajan result wang pei result kelley result

Wei Lu  1   ; Hourong Qin  1

1 Department of Mathematics Nanjing University 210093 Nanjing, China 
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Wei Lu; Hourong Qin. Eligible integers represented by positive ternary quadratic forms. Acta Arithmetica, Tome 179 (2017) no. 1, pp. 17-23. doi: 10.4064/aa8498-2-2017

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