Representation numbers of five sextenary quadratic forms

Ernest X. W. Xia, Olivia X. M. Yao, and A. F. Y. Zhao. "Representation numbers of five sextenary quadratic forms." Colloquium Mathematicae 138.2 (2015): 247-254. <http://eudml.org/doc/284018>.

@article{ErnestX2015,
abstract = {For nonnegative integers a, b, c and positive integer n, let N(a,b,c;n) denote the number of representations of n by the form $∑_\{i=1\}^\{a\} (x²_i + x_iy_i + y²_i) + 2∑_\{j=1\}^\{b\} (u²_j + u_jv_j + v²_j) + 4∑_\{k=1\}^\{c\} (r²_k + r_ks_k + s²_k)$. Explicit formulas for N(a,b,c;n) for some small values were determined by Alaca, Alaca and Williams, by Chan and Cooper, by Köklüce, and by Lomadze. We establish formulas for N(2,1,0;n), N(2,0,1;n), N(1,2,0;n), N(1,0,2;n) and N(1,1,1;n) by employing the (p, k)-parametrization of three 2-dimensional theta functions due to Alaca, Alaca and Williams.},
author = {Ernest X. W. Xia, Olivia X. M. Yao, A. F. Y. Zhao},
journal = {Colloquium Mathematicae},
keywords = {(p; k)-parametrization; quadratic form; 2-dimensional theta functions},
language = {eng},
number = {2},
pages = {247-254},
title = {Representation numbers of five sextenary quadratic forms},
url = {http://eudml.org/doc/284018},
volume = {138},
year = {2015},
}

TY - JOUR
AU - Ernest X. W. Xia
AU - Olivia X. M. Yao
AU - A. F. Y. Zhao
TI - Representation numbers of five sextenary quadratic forms
JO - Colloquium Mathematicae
PY - 2015
VL - 138
IS - 2
SP - 247
EP - 254
AB - For nonnegative integers a, b, c and positive integer n, let N(a,b,c;n) denote the number of representations of n by the form $∑_{i=1}^{a} (x²_i + x_iy_i + y²_i) + 2∑_{j=1}^{b} (u²_j + u_jv_j + v²_j) + 4∑_{k=1}^{c} (r²_k + r_ks_k + s²_k)$. Explicit formulas for N(a,b,c;n) for some small values were determined by Alaca, Alaca and Williams, by Chan and Cooper, by Köklüce, and by Lomadze. We establish formulas for N(2,1,0;n), N(2,0,1;n), N(1,2,0;n), N(1,0,2;n) and N(1,1,1;n) by employing the (p, k)-parametrization of three 2-dimensional theta functions due to Alaca, Alaca and Williams.
LA - eng
KW - (p; k)-parametrization; quadratic form; 2-dimensional theta functions
UR - http://eudml.org/doc/284018
ER -