Geodesic
Criteria for periodicity and an application to elliptic functions
Canadian mathematical bulletin, Tome 64 (2021) no. 3, pp. 530-540

Voir la notice de l'article provenant de la source Cambridge

DOI

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.
DOI : 10.4153/S0008439520000624
Mots-clés : Difference equations, periodic functions, elliptic functions 
Shalit, Ehud de. Criteria for periodicity and an application to elliptic functions. Canadian mathematical bulletin, Tome 64 (2021) no. 3, pp. 530-540. doi: 10.4153/S0008439520000624
@article{10_4153_S0008439520000624,
     author = {Shalit, Ehud de},
     title = {Criteria for periodicity and an application to elliptic functions},
     journal = {Canadian mathematical bulletin},
     pages = {530--540},
     year = {2021},
     volume = {64},
     number = {3},
     doi = {10.4153/S0008439520000624},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000624/}
}
TY  - JOUR
AU  - Shalit, Ehud de
TI  - Criteria for periodicity and an application to elliptic functions
JO  - Canadian mathematical bulletin
PY  - 2021
SP  - 530
EP  - 540
VL  - 64
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000624/
DO  - 10.4153/S0008439520000624
ID  - 10_4153_S0008439520000624
ER  - 
%0 Journal Article
%A Shalit, Ehud de
%T Criteria for periodicity and an application to elliptic functions
%J Canadian mathematical bulletin
%D 2021
%P 530-540
%V 64
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/S0008439520000624/
%R 10.4153/S0008439520000624
%F 10_4153_S0008439520000624

Cité par Sources :