On the number of representations of a positive integer by certain quadratic forms
Colloquium Mathematicum, Tome 135 (2014) no. 1, pp. 139-145
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
For natural numbers $a, b$ and positive integer $n$, let $R(a,b;n)$ denote the number of representations of $n$ in the form
$$ \sum _{i=1}^a (x_i^2+x_iy_i+y_i^2)+2\sum _{j=1}^b(u_j^2+u_jv_j+v_j^2). $$
Lomadze discovered a formula for $R(6,0;n)$. Explicit formulas for $R(1,5;n)$, $R(2,4;n)$, $R(3,3;n)$, $R(4,2;n)$ and $R(5,1;n)$ are determined in this paper by using the $(p; k)$-parametrization of theta functions due to Alaca, Alaca and Williams.
Keywords:
natural numbers positive integer n denote number representations form sum sum lomadze discovered formula explicit formulas determined paper using parametrization theta functions due alaca alaca williams
Affiliations des auteurs :
Ernest X. W. Xia 1
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author = {Ernest X. W. Xia},
title = {On the number of representations of a positive integer by certain quadratic forms},
journal = {Colloquium Mathematicum},
pages = {139--145},
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volume = {135},
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year = {2014},
doi = {10.4064/cm135-1-11},
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Ernest X. W. Xia. On the number of representations of a positive integer by certain quadratic forms. Colloquium Mathematicum, Tome 135 (2014) no. 1, pp. 139-145. doi: 10.4064/cm135-1-11
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