Adolf Hurwitz

Adolf Hurwitz (26 March 1859- 18 November 1919) was a German mathematician, and one of the most important figures in mathematics in the second half of the nineteenth century (according to Jean-Pierre Serre, 'always something good in Hurwitz'). He was born in a Jewish family in Hildesheim, and died in Zurich, in Switzerland. Download high resolution version (1000x1495, 120 KB)Adolf Hurwitz Copied from http://www-m1. ... Download high resolution version (1000x1495, 120 KB)Adolf Hurwitz Copied from http://www-m1. ... March 26 is the 85th day of the year in the Gregorian Calendar (86th in leap years). ... 1859 is a common year starting on Saturday. ... November 18 is the 322nd day of the year (323rd in leap years), with 43 remaining. ... 1919 (MCMXIX) was a common year starting on Wednesday (see link for calendar). ... Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... Jean-Pierre Serre (born September 15, 1926) is one of the leading mathematicians of the twentieth century, active in algebraic geometry, number theory and topology. ... â–¶(?) is a city in Lower Saxony, Germany. ... Location within Switzerland   Zürich[?] (German pronunciation IPA: ; usually spelled Zurich in English) is the largest city in Switzerland (population: 366,145 in 2004; population of urban area: 1,091,732) and capital of the canton of Zürich. ...

He was a doctoral student of Felix Klein in Leipzig, finishing a dissertation on elliptic modular functions in 1881. In 1884 he was offered a professorial position at Königsberg; there he encountered the young David Hilbert, on whom he had a major influence. He took a chair at the Eidgenössische Polytechnikum Zürich in 1892, and remained there for the rest of his life. Felix Christian Klein (April 25, 1849 – June 22, 1925) was a German mathematician. ... Leipzig â–¶(?) [] (Sorbian/Lusatian: Lipsk) is the largest city in the federal state (Bundesland) of Saxony in Germany. ... In mathematics, the j-invariant, regarded as a function of a complex variable τ, is a modular function defined on the upper half plane of complex numbers with positive imaginary part. ... 1881 was a common year starting on Saturday (see link for calendar). ... 1884 is a leap year starting on Tuesday (click on link to calendar). ... Map of Kaliningrad Oblast Kaliningrad (Russian: Калининград, German: Königsberg, Polish: Królewiec, Lithuanian: Karaliaučius, Latin: Regiomontium) is a seaport city, capital and main city of the Kaliningrad Oblast, the Russian exclave between Poland and Lithuania on the Baltic Sea. ... David Hilbert I was dreaming about a colony of spiders that lived behind a chair in my living room. ... ETH Zurich (from its German name Eidgenössische Technische Hochschule Zürich, ETHZ) is the Swiss Federal Institute of Technology in Zürich, Switzerland. ... 1892 was a leap year starting on Friday (see link for calendar). ...

He was one of the early masters of the Riemann surface theory, and used it to prove many of the foundational results on algebraic curves; for instance Hurwitz's automorphisms theorem. This work anticipates a number of later theories, such as the general theory of algebraic correspondences, Hecke operators, and Lefschetz fixed-point theorem. He also had deep interests in number theory. He studied the maximal order theory (as it now would be) for the quaternions, defining the Hurwitz quaternions that are now named for him. In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold. ... In algebraic geometry, an algebraic curve is an algebraic variety of dimension equal to 1. ... In mathematics, Hurwitzs automorphisms theorem bounds the group of automorphisms, via conformal mappings, of a compact Riemann surface of genus g > 1, telling us that the order of the group of such automorphisms is bounded by 84(g − 1). ... This article is in need of attention. ... In mathematics, in particular in the theory of modular forms, a Hecke operator is a certain kind of averaging operator that plays a significant role in the structure of vector spaces of modular forms (and more general automorphic representations). ... In mathematics, the Lefschetz fixed-point theorem counts the number of fixed points of a mapping from a topological space X to itself (subject to some mild conditions on X), by means of traces of the induced mappings on the homology groups of X. The counting is subject to some... Traditionally, number theory is the branch of pure mathematics concerned with the properties of integers. ... In mathematics, an order in the sense of ring theory in a ring R that is a finite-dimensional algebra over the rational number field Q is a subring O of R that satisfies the conditions O spans R over Q, so that QO = R; and O is a lattice... In mathematics, the quaternions are a non-commutative extension of the complex numbers. ... In mathematics, a Hurwitz quaternion (or Hurwitz integer) is a quaternion whose components are either all integers or all half-integers (a mixture of integers and half-integers is not allowed). ...

See also

• Riemann-Hurwitz formula
• Hurwitz matrix
• Hurwitz polynomial
• Hurwitz quaternion
• Hurwitz zeta function
• Hurwitz's automorphisms theorem
• Hurwitz's theorem

In mathematics, the Riemann-Hurwitz formula describes the relationship of the Euler characteristics of two surfaces when one is a ramified covering of the other. ... In mathematics, a square matrix is called a Hurwitz matrix if all eigenvalues of have strictly negative real part, that is, for each eigenvalue . ... A Hurwitz polynomial is a polynomial whose coefficients are positive real numbers and whose zeros are located in the left half-plane of the complex plane, that is, the real part of every zero is negative. ... In mathematics, a Hurwitz quaternion (or Hurwitz integer) is a quaternion whose components are either all integers or all half-integers (a mixture of integers and half-integers is not allowed). ... In mathematics, the Hurwitz zeta function is one of the many zeta functions. ... In mathematics, Hurwitzs automorphisms theorem bounds the group of automorphisms, via conformal mappings, of a compact Riemann surface of genus g > 1, telling us that the order of the group of such automorphisms is bounded by 84(g − 1). ... In mathematics, Hurwitzs theorem roughly states that, in certain conditions, if a sequence of holomorphic functions converges uniformly to a holomorphic function on compact sets, then after a while those functions and the limit function have the same number of zeros in any open disk. ...

External links

• LMS obituary
• Biography at the MacTutor archive