Related papers: Felix Klein's "On the eleventh degree transformati…
We present an English translation of a 1918 paper by Felix Klein.
We present an English translation of a third 1918 paper by Felix Klein which follows up on his earlier work.
We present an English translation of a second 1918 paper by Felix Klein which follows up on his earlier work.
This is an English translation of Felix Klein's classical paper "\"Uber die Aufl\"osung der allgemeinen Gleichungen f\"unften und sechsten Grades (Auszug aus einem Schreiben an Herrn K. Hensel)" from 1905 and is put in modern notation. The…
This is an English translation and digitisation of Frobenius' and Stickelberger's "On the theory of elliptic functions" first published in Journal fur die reine und angewandte Mathematik (Crelle's journal), 83, 175-179 (1877) with the title…
In 1989 H.Karcher rewrote the theory of elliptic functions through an approach that is much more geometrical than analytical. Therewith he obtained an optimal control over the behaviour and image values of these functions, which allowed for…
This is a translation of Kronecker's "\"Uber die Gleichungen f\"unften Grades" (On equations of fifth degree), excerpted from the monthly report to the Berlin Academy of Sciences from June 1861.
In his 1878/79 paper "Ueber die transformation siebenter ordnung der elliptischen functionen", Klein produced his famous 14-sided polygon representing the Klein quartic, his Riemann surface of genus 3 which has PSL(2,7) as its automorphism…
This is a literal word-for-word translation from the French of Phragmen's proof (the first such published) of Weierstrass' famous theorem characterizing all analytic functions which possess an algebraic addition theorem.
Felix Klein's so-called Erlangen Program was published in 1872 as professoral dissertation. It proposed a new solution to the problem how to classify and characterize geometries on the basis of projective geometry and group theory. The…
This is an English translation of the monograph "Die Klassenk\"orper der komplexen Multiplikation" by Max Deuring, published in 1958 as Enzyklop\"adie der Mathematischen Wissenschaften, Band I-2, Heft 10, Teil II by B.G. Teuber…
This is the paper "Niels Henrik Abel and the birth of fractional calculus", Podlubny, I., Magin, R. L., Trymorush I., Fractional Calculus and Applied Analysis, vol.20, no.5, pp.1068-1075, 2017 (https://doi.org/10.1515/fca-2017-0057) with…
In 1917 F. Klein proposed his work on projective geometry to A. Einstein for further developments of general relativity. Klein had a peculiar way to consider the relationship between mathematics and physics, based on his Erlanger Programm…
We present a rational version of the classical Landen transformation for elliptic integrals. This is employed to obtain explicit closed-form expressions for a large class of integrals of even rational functions and to develop an algorithm…
We present an exposition of the icosahedral solution of the quintic equation first described in Klein's classic work "Lectures on the icosahedron and the solution of equations of the fifth degree". Although we are heavily influenced by…
The goal of this modern presentation, followed by an English translation from the German, is to make available some parts of Lie's very systematic mathematical thought which deserve to join the contemporary literature, and above all also,…
This is a brief overview of the status of the theory of elliptic hypergeometric functions to the end of 2012 written as a complementary chapter to the Russian edition of the book by G.E. Andrews, R. Askey, and R. Roy, Special Functions,…
This version has been withdrawn. The new and final version is on ArXiv 1103.4878
This is the original paper appeared in the book "Elliptic and Parabolic Methods in Geometry (Minneapolis, MN,1994), A K Peters, Wellesley, MA, (1996)" (p.1-16), except with a few minor modifications as described at the end of the paper (on…
This is an English (annotated) translation of the German paper by Max Planck (1916) "On the absolute entropy of monatomic bodies" (\"Uber die absolute Entropie einatomiger K\"orper).