Journals / Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics / 2014 / Cilt: 63 - Sayı: 2
REPRESENTATION NUMBER FORMULAE FOR SOME OCTONARY QUADRATIC FORMS
- Journal
- Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
- Pages
- 135–145
- DOI
- —
Abstract
We find formulae for the number of representation of a positive integer n by each of the quadratic forms x21 + x22 + x23 + x24 + 2x25 + 2x26 + 6x27 + 6x28 , x21 + x22 + 2x23 + 2x24 + 2x25 + 2x26 + 3x27 + 3x28 , x21 + x22 + 3x23 + 3x24 + 6x25 + 6x26 + 6x27 + 6x28 , x21 + x22 + x23 + x24 + 2x25 + 2x26 + 3x27 + 3x28 , x21 + x22 + 2x23 + 2x24 + 2x25 + 2x26 + 6x27 + 6x28 , x21 + 2x22 + 2x23 + 2x24 + 2x25 + 4x26 + 6x27 + 6x28 , 2x21 + 2x22 + 3x23 + 6x24 + 6x25 + 6x26 + 6x27 + 12x28, by using some known convolution sums of divisor functions and known repre- sentation formulae for quaternary quadratic forms. Formulae for some other octonary quadratic forms of these type are given before in [4, 5, 6, 11, 17].