Representation numbers of five sextenary quadratic forms

• Autorzy: Ernest X. W. Xia , Olivia X. M. Yao , A. F. Y. Zhao
• Języki publikacji: EN

Abstrakty

EN

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.

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: 2015
• Tom: 138
• Numer: 2
• Strony: 247-254

Daty

wydano

2015

Twórcy

autor

Ernest X. W. Xia

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

autor

Olivia X. M. Yao

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

autor

A. F. Y. Zhao

• School of Mathematical Sciences, and Institute of Mathematics, Nanjing Normal University, Nanjing 210023, P. R. China

Identyfikatory

DOI

10.4064/cm138-2-9