Algebraic Functions of Complexity One, a Weierstrass Theorem and Three Arithmetic Operationsстатья
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Дата последнего поиска статьи во внешних источниках: 26 сентября 2016 г.
Местоположение издательства:Road Town, United Kingdom
Первая страница:343
Последняя страница:347
Аннотация:The Weierstrass theorem concerning the functions admitting an algebraic addition
theorem enables us to give an explicit description of algebraic functions of two variables of
analytical complexity one. Their description is divided into three cases: the general case, which
is elliptic, and two special ones, a multiplicative and and additive. All cases have a unified
description; these are the orbits of an action of the gauge pseudogroup. The first case is a 1-
parameter family of orbits of “elliptic addition,” the second is the orbit of multiplication, and
the third of addition. Here the multiplication and addition can be derived from the “elliptic
addition” by passages to a limit. On the other hand, the elliptic orbits correspond to complex
structures on the torus, the multiplicative orbit corresponds to the complex structure on the
cylinder, and the additive one to that on the complex plane.
This work was financially supported by the Russian Foundation for Basic Research under
grants nos. 13-01-12417-a and 14-01-00709-ofi-i-2013.