Eisenstein series part of the primitive representations for even rank quadratic forms
Number Theory
2024-11-27 v2
Abstract
In this paper, we first investigate the relationship between the number of primitive representations of by quadratic forms and the number of non-primitive ones. We hence obtain a theorem to deal with the Eisenstein series part with quadratic Dirichlet character when deriving the formula for the number of primitive representations of an integer by even rank quadratic forms from the number of non primitive ones. Formulas for special cases are given as examples.
Keywords
Cite
@article{arxiv.2303.18071,
title = {Eisenstein series part of the primitive representations for even rank quadratic forms},
author = {Ben Kane and Luhao Xue},
journal= {arXiv preprint arXiv:2303.18071},
year = {2024}
}