Subfields of index 2 of elliptic function fields

1973 ◽  
pp. 171-193
Author(s):  
R. E. MacRae ◽  
Pierre Samuel
Keyword(s):  
Elliptic Function ◽  
Function Fields ◽  
Index 2

scholarly journals Criteria for periodicity and an application to elliptic functions

2020 ◽  
pp. 1-11
Author(s):  
Ehud de Shalit
Keyword(s):  
Vector Space ◽  
Elliptic Function ◽  
Function Fields ◽  
Elliptic Functions ◽  
Real Vector Space ◽  
Real Vector ◽  
Finite Dimensional ◽  
Full Discussion ◽  
Rank 2 ◽  
Higher Rank

Abstract Let P and Q be relatively prime integers greater than 1, and let f be a real valued discretely supported function on a finite dimensional real vector space V. We prove that if $f_{P}(x)=f(Px)-f(x)$ and $f_{Q}(x)=f(Qx)-f(x)$ are both $\Lambda $ -periodic for some lattice $\Lambda \subset V$ , then so is f (up to a modification at $0$ ). This result is used to prove a theorem on the arithmetic of elliptic function fields. In the last section, we discuss the higher rank analogue of this theorem and explain why it fails in rank 2. A full discussion of the higher rank case will appear in a forthcoming work.

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