2024/12/08 by Kiyoshi Sogo, Sogo, Kiyoshi
Mathematics · #Advanced Mathematical Identities
paper · pdf · doi:10.48550/arxiv.2412.06076
Jacobi's theta relations among quartic products of theta functions are generalized to those of arbitrary n products. Igusa's procedure of derivation is extended to prove such general theta relations, from which we obtain general addition formulas and theta constants identities. To complete the proof, the concept of \it cycle number λ is essential. The case of n=3 is discussed and examined explicitly.