On the number of representations of a positive integer by certain quadratic forms
Tom 135 / 2014
Colloquium Mathematicum 135 (2014), 139-145
MSC: Primary 11E25; Secondary 11E20, 11A25.
DOI: 10.4064/cm135-1-11
Streszczenie
For natural numbers 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.
