• Thumbnail for Ernst Kummer
    Ernst Eduard Kummer (29 January 1810 – 14 May 1893) was a German mathematician. Skilled in applied mathematics, Kummer trained German army officers in...
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  • American actress Ernst Kummer (1810–1893), German mathematician Kummer configuration, a mathematical structure discovered by Ernst Kummer Kummer surface, a...
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  • Thumbnail for Fermat's Last Theorem
    Ernst Kummer extended this and proved the theorem for all regular primes, leaving irregular primes to be analyzed individually. Building on Kummer's work...
    103 KB (11,486 words) - 13:37, 19 November 2024
  • Thumbnail for Kummer surface
    In algebraic geometry, a Kummer quartic surface, first studied by Ernst Kummer (1864), is an irreducible nodal surface of degree 4 in P 3 {\displaystyle...
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  • binomial coefficient. The theorem is named after Ernst Kummer, who proved it in a paper, (Kummer 1852). Kummer's theorem states that for given integers n ≥ m ≥ 0...
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  • after Richard Dedekind who developed the theorem based on the work of Ernst Kummer.[citation needed][when?] Let K {\displaystyle K} be a number field such...
    3 KB (560 words) - 07:41, 14 December 2024
  • defined below, is related to the polylogarithm. Both are named for Ernst Kummer. Kummer's function is defined by Λ n ( z ) = ∫ 0 z log n − 1 ⁡ | t | 1 + t...
    1 KB (241 words) - 16:25, 11 September 2023
  • theory, a regular prime is a special kind of prime number, defined by Ernst Kummer in 1850 to prove certain cases of Fermat's Last Theorem. Regular primes...
    29 KB (3,270 words) - 15:24, 15 October 2024
  • Thumbnail for Hypergeometric function
    Friedrich Gauss (1813). Studies in the nineteenth century included those of Ernst Kummer (1836), and the fundamental characterisation by Bernhard Riemann (1857)...
    38 KB (6,914 words) - 09:18, 30 November 2024
  • war crimes Ernst Keil (1816–1878), German publisher Ernst af Klercker (1881–1955), Swedish general Ernst Kummer, German mathematician Ernst Laraque, Haitian...
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  • Thumbnail for Leopold Kronecker
    is the work of man"). Kronecker was a student and life-long friend of Ernst Kummer. Leopold Kronecker was born on 7 December 1823 in Liegnitz, Prussia (now...
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  • conjecture was first made by Ernst Kummer on 28 December 1849 and 24 April 1853 in letters to Leopold Kronecker, reprinted in (Kummer 1975, pages 84, 93, 123–124)...
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  • Thumbnail for Arthur Moritz Schoenflies
    Schoenflies married Emma Levin (1868–1939) in 1896. He studied under Ernst Kummer and Karl Weierstrass, and was influenced by Felix Klein. The Schoenflies...
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  • Thumbnail for Hans Carl Friedrich von Mangoldt
    (Ph.D) in 1878 at the University of Berlin, where his supervisors were Ernst Kummer and Karl Weierstrass. He contributed to the solution of the prime number...
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  • Thumbnail for Wilhelm Killing
    Münster and later wrote his dissertation under Karl Weierstrass and Ernst Kummer at Berlin in 1872. He taught in gymnasia (secondary schools) from 1868...
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  • Thumbnail for Hermann Schwarz
    Sobieszów, Poland). In 1868 he married Marie Kummer, who was the daughter to the mathematician Ernst Eduard Kummer and Ottilie née Mendelssohn (a daughter...
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  • analysis, Kummer's transformation of series is a method used to accelerate the convergence of an infinite series. The method was first suggested by Ernst Kummer...
    4 KB (861 words) - 18:46, 28 November 2023
  • Thumbnail for Elwin Bruno Christoffel
    electricity in homogeneous bodies written under the supervision of Martin Ohm, Ernst Kummer and Heinrich Gustav Magnus. After receiving his doctorate, Christoffel...
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  • the failure of unique factorization in their rings of integers – that Ernst Kummer first introduced the concept of an ideal number and proved his celebrated...
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  • Thumbnail for Heinrich Scherk
    distribution of prime numbers. He is also notable as the doctoral advisor of Ernst Kummer. (in German) Biography of Scherk Heinrich Scherk at the Mathematics Genealogy...
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  • in the ring of integers of a number field; the idea was developed by Ernst Kummer, and led to Richard Dedekind's definition of ideals for rings. An ideal...
    7 KB (1,226 words) - 16:48, 31 October 2024
  • Diverge if ρ ≤ 1 {\displaystyle \rho \leq 1} This extension is due to Ernst Kummer. Let ζn be an auxiliary sequence of positive constants. Define ρ n ≡...
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  • class groups of cyclotomic fields. A special case was first proven by Ernst Kummer (1847) while the general result is due to Ludwig Stickelberger (1890)...
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  • Kummer sum is the name given to certain cubic Gauss sums for a prime modulus p, with p congruent to 1 modulo 3. They are named after Ernst Kummer, who...
    7 KB (1,068 words) - 04:43, 29 November 2022
  • elements of the base field. The theory was originally developed by Ernst Eduard Kummer around the 1840s in his pioneering work on Fermat's Last Theorem...
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  • Thumbnail for Hermann Grassmann
    university position, whereupon that Ministry asked Ernst Kummer for his opinion of Grassmann. Kummer wrote back saying that Grassmann's 1846 prize essay...
    28 KB (3,197 words) - 23:50, 10 November 2024
  • Thumbnail for Georg Cantor
    Berlin, attending lectures by Leopold Kronecker, Karl Weierstrass and Ernst Kummer. He spent the summer of 1866 at the University of Göttingen, then and...
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  • Thumbnail for Otto Hölder
    Berlin where he was a student of Leopold Kronecker, Karl Weierstrass, and Ernst Kummer. In 1877, he entered the University of Berlin and took his doctorate...
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  • Thumbnail for Ferdinand Georg Frobenius
    semester before returning to Berlin, where he attended lectures by Kronecker, Kummer and Karl Weierstrass. He received his doctorate (awarded with distinction)...
    14 KB (1,445 words) - 19:10, 23 September 2024
  • the class group of certain number fields. It is a strengthening of Ernst Kummer's theorem to the effect that the prime p divides the class number of the...
    6 KB (776 words) - 01:16, 16 October 2024