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

Ernest X. W. Xia

Colloquium Mathematicae, Tome 135 (2014), p. 139-145 / Harvested from The Polish Digital Mathematics Library

Résumé

For natural numbers a,b and positive integer n, let R(a,b;n) denote the number of representations of n in the form $\sum_{i = 1}^{a} (x ²_{i} + x_{i} y_{i} + y ²_{i}) + 2 \sum_{j = 1}^{b} (u ²_{j} + u_{j} v_{j} + v ²_{j})$ . 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.

Publié le : 2014-01-01

Zbl 1294.11043

EUDML-ID : urn:eudml:doc:283763

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     title = {On the number of representations of a positive integer by certain quadratic forms},
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     volume = {135},
     year = {2014},
     pages = {139-145},
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     language = {en},
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Ernest X. W. Xia. On the number of representations of a positive integer by certain quadratic forms. Colloquium Mathematicae, Tome 135 (2014) pp. 139-145. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm135-1-11/