English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

1. Abelian functions by Poincaré. 1-1. If the variable x and a general solution y of a linear differential equation with polynomial coefficients are algebraically dependent, the periods of abelian integrals of the first kind associated with the curve f(x, y) = 0 satisfy certain relations. In his earliest works on abelian functions Poincaré examined such relations in some special cases. He also used a similar relation in a joint paper with Picard of 1883 on a "theorem of Riemann". Poincaré later developed a general theory of reducible integrals. This theory played some role in almost all of his works on abelian functions. We shall start by recalling the theorem of Riemann: There are three related theorems concerning a complex torus. If ƒ is a meromorphic function on C, an element a of C such that f(z + a) = f(z) for a variable z in C* is called a period off; the set of all periods of ƒ forms a closed subgroup of C, called the period group of ƒ. Let A denote a lattice in C*, i.e., a discrete subgroup of C with compact quotient; then a meromorphic function ƒ on C whose period group contains A, i.e., a meromorphic function on the complex torus T = C*/A considered as a function on C, is called an abelian function relative to A and a holomorphic function ® on C with the property

Problems on Abelian functions at the time of Poincaré and some at present