sigma functions
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Axioms ◽  
2021 ◽  
Vol 11 (1) ◽  
pp. 12
Author(s):  
Mykola Korenkov ◽  
Yurii Kharkevych

A refined asymptotics of the Jacobi theta functions and their logarithmic derivatives have been received. The asymptotics of the Nevanlinna characteristics of the indicated functions and the arbitrary elliptic function have been found. The estimation of the type of the Weierstrass sigma functions has been given.


2021 ◽  
Vol 872 (1) ◽  
pp. 012009
Author(s):  
E A Shakhray ◽  
E V Lubentsova ◽  
V F Lubentsov ◽  
N A Styrkhunova

2019 ◽  
Vol 243 (6) ◽  
pp. 872-879
Author(s):  
A. A. Illarionov
Keyword(s):  

2019 ◽  
Vol 53 (3) ◽  
pp. 157-173
Author(s):  
T. Ayano ◽  
V. M. Buchstaber

2018 ◽  
Vol 61 (1) ◽  
pp. 169-193 ◽  
Author(s):  
JULIA BERNATSKA ◽  
DMITRY LEYKIN

AbstractWe obtain explicit expressions for genus 2 degenerate sigma-function in terms of genus 1 sigma-function and elementary functions as solutions of a system of linear partial differential equations satisfied by the sigma-function. By way of application, we derive a solution for a class of generalized Jacobi inversion problems on elliptic curves, a family of Schrödinger-type operators on a line with common spectrum consisting of a point and two segments, explicit construction of a field of three-periodic meromorphic functions. Generators of rank 3 lattice in ℂ2are given explicitly.


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