Geodesic
On the connection between hyperelliptic systems of sequences and functions
Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 2, pp. 210-220

Voir la notice de l'article provenant de la source Math-Net.Ru

We study the connection between $1$-periodic solutions of the functional equation $$ f(x+y)g(x-y)=\sum_{j=1}^N\varphi_j(x)\psi_j(y) \quad (x,y\in \mathbb C) $$ and some sequences of special kind. As an application we solve the equation in the case when $g$ is Jacobi theta function. 
@article{DVMG_2017_17_2_a8,
     author = {A. A. Illarionov and M. A. Romanov},
     title = {On the connection between hyperelliptic systems of sequences and functions},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {210--220},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2017_17_2_a8/}
}
TY  - JOUR
AU  - A. A. Illarionov
AU  - M. A. Romanov
TI  - On the connection between hyperelliptic systems of sequences and functions
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2017
SP  - 210
EP  - 220
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2017_17_2_a8/
LA  - ru
ID  - DVMG_2017_17_2_a8
ER  - 
%0 Journal Article
%A A. A. Illarionov
%A M. A. Romanov
%T On the connection between hyperelliptic systems of sequences and functions
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2017
%P 210-220
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2017_17_2_a8/
%G ru
%F DVMG_2017_17_2_a8
A. A. Illarionov; M. A. Romanov. On the connection between hyperelliptic systems of sequences and functions. Dalʹnevostočnyj matematičeskij žurnal, Tome 17 (2017) no. 2, pp. 210-220. http://geodesic.mathdoc.fr/item/DVMG_2017_17_2_a8/