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Representation numbers of five sextenary quadratic forms

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Xia E., Yao O., Zhao A.

Colloquium Mathematicum

2015

tom 138

nr 2

247-254

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Xia E.

1 Yao O.

1 Zhao A.

1 2015

Wyniki wyszukiwania

Representation numbers of five sextenary quadratic forms