On Products of Weierstrass Sigma Functions

We prove the following result. Let f : C → C be an even entire function. Assume that there exist α j , β j : C → C with f x + y f x − y = ∑ j = 1 4 α j x β j y , x , y ∈ C . Then f ( z ) = σL ( z ) · σΛ ( z ) · e Az 2+ C where L and Λ are lattices in C, σ L is the Weierstrass sigma function assoc...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-03, Vol.243 (6), p.872-879
Main Author: Illarionov, A. A.
Format: Article
Language:English
Subjects:
Entire functions
Lattices
Mathematics
Mathematics and Statistics
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove the following result. Let f : C → C be an even entire function. Assume that there exist α j , β j : C → C with f x + y f x − y = ∑ j = 1 4 α j x β j y , x , y ∈ C . Then f ( z ) = σL ( z ) · σΛ ( z ) · e Az 2+ C where L and Λ are lattices in C, σ L is the Weierstrass sigma function associated with the lattice L , and A,C ∈ C.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04587-1