Representations by sexternary quadratic forms with coefficients 1,2,5 and 10

Bülent Köklüce

Representations by sexternary quadratic forms with coefficients 1,2,5 and 10

Number Theory 2022-07-13 v1

Authors: Bülent Köklüce

Abstract

In this article, we find bases for the spaces of modular forms $M_{3}(\Gamma _{0}(40),\left( \frac{d}{\cdot }\right) )$ for $d=-4,-8,-20\text{ and }-40.$ We then derive formulas for the number of representations of a positive integer by all the diagonal sextenary quadratic forms with coefficients $% 1,2,5$ and $10$ .

Keywords

modular forms sextenary quadratic forms representation numbers gamma_0 congruence subgroup dirichlet character

Cite

@article{arxiv.2207.05638,
  title  = {Representations by sexternary quadratic forms with coefficients 1,2,5 and 10},
  author = {Bülent Köklüce},
  journal= {arXiv preprint arXiv:2207.05638},
  year   = {2022}
}

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