Elliptic functions in signature four
英文摘要：
We explore the relationships between two elliptic functions constructed by Shen in the signature four Ramanujan theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
相关论文
Hypergeometric identities in elliptic signature six
Within the Ramanujan theories of elliptic functions, Li-Chien Shen constructed natural elliptic functions in signature three and signature four. When applied in signature six, the same constructions produce non-elliptic functions that nevertheless engender the corresponding hypergeometric identities of Ramanujan.
math.CV
A root elliptic function in signature four
We present a new approach to elliptic functions in signature four, offering a fresh perspective on work of Li-Chien Shen.
math.CAmath.CV
The Berndt-Bhargava-Garvan Transfer Principle for signature three
We offer a new proof for the Berndt-Bhargava-Garvan Transfer Principle that connects the signature-three elliptic theory of Ramanujan to the classical elliptic theory.
math.CV
On Weierstrass $\wp$ in signature 3
In his work on the Ramanujan theory of elliptic functions to alternative bases, Shen constructed two different elliptic functions in signature three; we determine the precise relationship between them, by precisely relating their coperiodic Weierstrass $\wp$ functions.
math.CV
Elliptic functions from hypergeometric integrals
As a contribution to the Ramanujan theory of elliptic functions to alternative bases, Li-Chien Shen has shown how analogues of the Jacobian elliptic functions may be derived from incomplete hypergeometric integrals in signatures three and four. We determine precisely the signatures in which the Jacobian analogues or their squares are indeed elliptic.
math.CAmath.CV
The elliptic function ${\rm dn}_2$ of Shen
We analyze the elliptic function ${\rm dn}_2$ introduced by Li-Chien Shen, contributing to the Ramanujan theory of elliptic functions in signature four.
math.CV
更多相关论文收起更多论文
The elliptic function ${\rm dn}_3$ of Shen
We analyze the elliptic function ${\rm dn}_3$ introduced by Li-Chien Shen, contributing to the Ramanujan theory of elliptic functions in signature three. A famous hypergeometric identity emerges from our analysis.
math.CV
Signatures of Branched Coverings
In this paper we deal with branched coverings over the complement to finitely many exceptional points on the Riemann sphere having the property that the local monodromy around each of the branching points is of finite order. To such a covering we assign its \textit{signature}, i.e. the set of its exceptional and branching points together with the orders of local monodromy operators around the branching points. What can be said about the monodromy group of a branched covering if its signature is known? It seems at first that the answer is nothing or next to nothing. Indeed, generically it is so…
math.AGmath.CV
Some remarks on the correspondence between elliptic curves and four points in the Riemann sphere
In this paper we relate some classical normal forms for complex elliptic curves in terms of 4-point sets in the Riemann sphere. Our main result is an alternative proof that every elliptic curve is isomorphic as a Riemann surface to one in the Hesse normal form. In this setting, we give an alternative proof of the equivalence between the Edwards and the Jacobi normal forms. Also, we give a geometric construction of the cross ratios for 4-point sets in general position.
math.CV
Equivalence of two canonical lists of elliptic functions
We establish a one-to-one correspondence between,on one hand the four types of transcendental meromorphic solutions of the autonomous Schwarzian differential equations which are elliptic,on the other hand the four binomial equations of Briot and Bouquet possessing an elliptic solution.
math.CAmath.CVnlin.SI
