Representations by octonary quadratic forms with coefficients $1$ , $2$ , $3$ or $6$

preprint2016arXivOpen access

Using modular forms we determine formulas for the number of representations of a positive integer by diagonal octonary quadratic forms with coefficients $1$ , $2$ , $3$ or $6$ .

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Representations by octonary quadratic forms with coefficients $1$ , $2$ , $3$ or $6$

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Representations by octonary quadratic forms with coefficients 111, 222, 333 or 666

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Representations by octonary quadratic forms with coefficients $1$ , $2$ , $3$ or $6$