On the number of representations of a positive integer by certain quadratic forms

Ernest X. W. Xia. "On the number of representations of a positive integer by certain quadratic forms." Colloquium Mathematicae 135.1 (2014): 139-145. <http://eudml.org/doc/283763>.

@article{ErnestX2014,
abstract = {For natural numbers a,b and positive integer n, let R(a,b;n) denote the number of representations of n in the form $∑_\{i=1\}^\{a\} (x²_i + x_iy_i + y²_i) + 2∑_\{j=1\}^\{b\} (u²_j + u_jv_j + v²_j)$. 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.},
author = {Ernest X. W. Xia},
journal = {Colloquium Mathematicae},
keywords = {Eisenstein series; ; k); sum of divisors function; quadratic form},
language = {eng},
number = {1},
pages = {139-145},
title = {On the number of representations of a positive integer by certain quadratic forms},
url = {http://eudml.org/doc/283763},
volume = {135},
year = {2014},
}

TY - JOUR
AU - Ernest X. W. Xia
TI - On the number of representations of a positive integer by certain quadratic forms
JO - Colloquium Mathematicae
PY - 2014
VL - 135
IS - 1
SP - 139
EP - 145
AB - For natural numbers a,b and positive integer n, let R(a,b;n) denote the number of representations of n in the form $∑_{i=1}^{a} (x²_i + x_iy_i + y²_i) + 2∑_{j=1}^{b} (u²_j + u_jv_j + v²_j)$. 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.
LA - eng
KW - Eisenstein series; ; k); sum of divisors function; quadratic form
UR - http://eudml.org/doc/283763
ER -