论文标题
kronecker theta函数和theta函数的分解定理i
Kronecker theta function and a decomposition theorem for theta functions I
论文作者
论文摘要
Kronecker Theta功能是Jacobi Theta函数的商，这也是Ramanujan的$_1ψ_1$ Sumpation的特殊情况。使用kronecker theta函数作为构建块，我们证明了theta函数的分解定理。该分解定理是大量theta函数身份的共同来源。许多引人注目的theta函数身份，无论是经典还是新的，都是从该分解定理得出的。建立了一个新的theta功能的添加公式。由于Ramanujan，Weierstrass，Kiepert，Winquist和Shen等引起的椭圆形功能理论的几个已知结果。奇怪的是三角的身份。
The Kronecker theta function is a quotient of the Jacobi theta functions, which is also a special case of Ramanujan's $_1ψ_1$ summation. Using the Kronecker theta function as building blocks, we prove a decomposition theorem for theta functions. This decomposition theorem is the common source of a large number of theta function identities. Many striking theta function identities, both classical and new, are derived from this decomposition theorem with ease. A new addition formula for theta functions is established. Several known results in the theory of elliptic theta functions due to Ramanujan, Weierstrass, Kiepert, Winquist and Shen among others are revisited. A curious trigonometric identities is proved.
