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- Title
REPRESENTATION NUMBER FORMULAE FOR SOME OCTONARY QUADRATIC FORMS.
- Authors
KÖKLÜCE, BÜLENT
- Abstract
We find formulae for the number of representation of a positive integer n by each of the quadratic forms x12 + x22 + x32+ x42 + 2x52 + 2x62+ 6x72 + 6x82, x12+ x22 + 2x32 + 2x42 + 2x52 + 2x62+ 3x72 + 3x82, x12 + x22 + 3x32 + 3x42 + 6x52+ 6x62 + 6x72 + 6x82, x12 + x22 + x32 + x42 + 2x52+ 2x62 + 3x72+ 3x82, x12 + x22 + 2x32 + 2x42 + 2x52 + 2x62 + 6x72 + 6x82, x12 + 2x22 + 2x32 + 2x42 + 2x52 + 4x62 + 6x72 + 6x82, 2x12 + 2x22 + 3x32 + 6x42+ 6x52 + 6x62 + 6x72 + 12x82, 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].
- Subjects
MATHEMATICAL formulas; QUATERNARY forms; QUADRATIC equations; INTEGERS; MATHEMATICAL convolutions
- Publication
Communications Series A1 Mathematics & Statistics, 2014, Vol 63, Issue 2, p135
- ISSN
1303-5991
- Publication type
Article