Representation numbers of five sextenary quadratic forms

Ernest X. W. Xia; Olivia X. M. Yao; A. F. Y. Zhao

Ernest X. W. Xia ; Olivia X. M. Yao ; A. F. Y. Zhao

Colloquium Mathematicae, Tome 139 (2015), p. 247-254 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $\sum_{i = 1}^{a} (x ²_{i} + x_{i} y_{i} + y ²_{i}) + 2 \sum_{j = 1}^{b} (u ²_{j} + u_{j} v_{j} + v ²_{j}) + 4 \sum_{k = 1}^{c} (r ²_{k} + r_{k} s_{k} + s ²_{k})$ . 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.

Publié le : 2015-01-01

Zbl 06401029

EUDML-ID : urn:eudml:doc:284018

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     title = {Representation numbers of five sextenary quadratic forms},
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     year = {2015},
     pages = {247-254},
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Ernest X. W. Xia; Olivia X. M. Yao; A. F. Y. Zhao. Representation numbers of five sextenary quadratic forms. Colloquium Mathematicae, Tome 139 (2015) pp. 247-254. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm138-2-9/