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math.NT2014★ 2 cited
On certain quaternary quadratic forms
Kazuhide Matsuda
In this paper, we determine all the positive integers and such that every nonnegative integer can be represented as $$ f^{a,b}_c(x,y,z,w)=ax^2+by^2+c(z^2+zw+w^2) \,\, \t…
math.NT2014
Analogues of Jacobi's derivative formula
Kazuhide Matsuda
In this paper, we obtain analogues of Jacobi's derivative formula in terms of the theta constants with rational characteristics. For this purpose, we use the arithmetic formulas of…