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REPRESENTATION NUMBER FORMULAE FOR SOME OCTONARY QUADRATIC FORMS
Journal article   Open access   Peer reviewed

REPRESENTATION NUMBER FORMULAE FOR SOME OCTONARY QUADRATIC FORMS

Bulent Kokluce
Communications Series A1 Mathematics & Statistics, Vol.63(2), pp.135-145
02/2014
DOI: https://doi.org/10.1501/Commua1_0000000719

Abstract

Mathematics Physical Sciences Science & Technology
We find formulae for the number of representation of a positive integer n by each of the quadratic forms x(1)(2) + x(2)(2) + x(3)(2)+ x(4)(2) + 2x(5)(2) + 2x(6)(2) + 6x(7)(2) + 6x(8)(2), x(1)(2) + x(2)(2) + 2x(3)(2)+ 2x(4)(2) + 2x(5)(2) + 2x(6)(2) + 3x(7)(2) + 3x(8)(2), x(1)(2) + x(2)(2) + 3x(3)(2)+ 3x(4)(2) + 6x(5)(2) + 6x(6)(2) + 6x(7)(2) + 6x(8)(2), x(1)(2) + x(2)(2) + x(3)(2)+ x(4)(2) + 2x(5)(2) + 2x(6)(2) + 3x(7)(2) + 3x(8)(2), x(1)(2) + x(2)(2) + 2x(3)(2)+ 2x(4)(2) + 2x(5)(2) + 2x(6)(2) + 6x(7)(2) + 6x(8)(2), x(1)(2) + 2x(2)(2) + 2x(3)(2)+ 2x(4)(2) + 2x(5)(2) + 4x(6)(2) + 6x(7)(2) + 6x(8)(2), 2x(1)(2) + 2x(2)(2) + 3x(3)(2)+ 6x(4)(2) + 6x(5)(2) + 6x(6)(2) + 6x(7)(2) + 12x(8)(2), by using some known convolution sums of divisor functions and known representation formulae for quaternary quadratic forms. Formulae for some other octonary quadratic forms of these type are given before in [4, 5, 6, 11, 17].
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https://doi.org/10.1501/Commua1_0000000719View
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