Cherng-Tiao Perng

Affiliation: Norfolk State University

Email: ctperng@nsu.edu

Title Of Talk: Factorization of Quaternions of Lipschitz types and its application to Jacobi's formulas for the number of representations

Abstract: Using quaternions of Lipschitz types, we study three quaternary quadratic forms including the most classical one which is a diagonal form with coefficients $(1,1,1,1)$. Based on our factorization theory of these quaternions, we proved the associated formulas of Jacobi types for the number of representations in the corresponding quadratic forms. Note that the formulas associated with the other two forms with coefficients $(1,1,2,2)$ and $(1,1,3,3)$ are usually called formulas of Liouville types. J. Deutch proved the case for $(1,1,2,2)$ using an analogue of Hurwitz quaternions. Reversing history, we proved all three by quaternions of Lipschitz types, based on Euler's algorithm.

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