A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Eligible integers represented by positive ternary quadratic forms

Volume 179 / 2017

Wei Lu, Hourong Qin Acta Arithmetica 179 (2017), 17-23 MSC: 11E20, 11F37. DOI: 10.4064/aa8498-2-2017 Published online: 24 May 2017

Abstract

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 $f=x_1^2+x_2^2+7x_3^2$.

Authors

  • Wei LuDepartment of Mathematics
    Nanjing University
    210093 Nanjing, China
    e-mail
  • Hourong QinDepartment of Mathematics
    Nanjing University
    210093 Nanjing, China
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image