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

• Autorzy: Ernest X. W. Xia
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11A25: Arithmetic functions; related numbers; inversion formulas
• 11E20: General ternary and quaternary quadratic forms; forms of more than two variables
• 11E25: Sums of squares and representations by other particular quadratic forms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2014
• Tom: 135
• Numer: 1
• Strony: 139-145

Daty

wydano

2014

Twórcy

autor

Ernest X. W. Xia

• Department of Mathematics, Jiangsu University, Zhenjiang, Jiangsu 212013, P.R. China

Identyfikatory

DOI

10.4064/cm135-1-11