The (p, k)-parametrization of theta functions introduced by the authors is usedto prove some new theta function identities from which formulae for the number ofrepresentations of a positive integer by each of the sextenary quadratic forms. x2 1+x2 2+x2 3+x2 4+x2 5+3x2 6, x2 1+x2 2+x2 3+3x2 4+3x2 5+3x2 6 and x2 1+3x2 2+3x2 3+3x2 4+3x2 5+3x2 6 are deduced.

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Keywords (p, k)-parametrization of theta functions, Representations by sextenary quadratic forms, Theta function identities
Alaca, A, Alaca, S, & Williams, K.S. (2011). Some new theta function identitieswith applications to sextenaryquadratic forms. In Frontiers of Combinatorics and Number Theory (pp. 91–102).