Gauss (1813). Studies in the nineteenth century included those of Ernst Kummer (1836), and the fundamental characterisation by Bernhard Riemann (1857)...

Ernst Kummer extended this and proved the theorem for all regular primes, leaving irregular primes to be analyzed individually. Building on Kummer's work...

{1}{p-1}}\left(n-s_{p}(n)\right).\end{aligned}}} Legendre's formula can be used to prove Kummer's theorem. As one special case, it can be used to prove that if n is a positive...

2017-02-02. Désarménien, Jacques (March 1982). "Un Analogue des Congruences de Kummer pour les q-nombres d'Euler". European Journal of Combinatorics. 3 (1):...

of Charles Mangin. Application de la théorie des fonctions fuchsiennes à l'étude des courbes algébriques, Journal de mathematiques pure et appliquées...

{p^{n}}{q}}\right\}} where n is some integer prime to l such that pn is principal. The Kummer reciprocity law states that { p q } = { q p } {\displaystyle \left\{{\frac...

Allgemeine Theorie der algebraischen Zahlen. Vol. 8. Teubner, 1953. Eisenstein reciprocity Hilbert class field Keller's conjecture Kummer–Vandiver conjecture...

cyclic extensions of fields (or to one of its generalizations) that leads to Kummer theory. In its most basic form, it states that if L/K is an extension of...

so-called Kummer spaces. Whittaker functions appear as coefficients of certain representations of the group SL2(R), called Whittaker models. Louis de Branges...

university position, whereupon that Ministry asked Ernst Kummer for his opinion of Grassmann. Kummer wrote back saying that Grassmann's 1846 prize essay (see...

year 1877–1878 at the University of Berlin where he attended classes by Kummer, Weierstrass and Kronecker, after which he returned to Munich. In October...

for lth power residues (theorem 140) . Part 5 covers Kummer number fields, and ends with Kummer's proof of Fermat's last theorem for regular primes. Brill...

Eduard Kummer's ideal numbers, devised as part of Kummer's 1843 attempt to prove Fermat's Last Theorem. (Thus Dedekind can be said to have been Kummer's most...

Richelot, the Richelot isogeny. 1847 Adolph Göpel gives the equation of the Kummer surface 1851 Johann Georg Rosenhain writes a prize essay on the inversion...

he discovered the fundamental properties of the asymptotic lines on the Kummer surface. They later investigated W-curves, curves invariant under a group...

Grothendieck; Jean-Louis Verdier (eds.), Séminaire de Géométrie Algébrique du Bois Marie – 1963–64 – Théorie des topos et cohomologie étale des schémas – (SGA...

semester before returning to Berlin, where he attended lectures by Kronecker, Kummer, and Karl Weierstrass. He received his doctorate (awarded with distinction)...

interpolation of special values of L-functions. For example, Kubota–Leopoldt used Kummer's congruences for Bernoulli numbers to construct a p-adic L-function, the...

than half of his famous Zahlbericht is little more than an account of Kummer's number-theoretical work, with inessential improvements") and Emmy Noether...

= 0 for higher values of k. This generalization is largely due to Ernst Kummer, who also invented ideal numbers, which were expressed as geometrical entities...

surface des ondes." Journal de Mathématiques Pures et Appliquées 11 (1846): 291-296. Dolgachev, Igor (2019-10-16). "Kummer surfaces: 200 years of study"...

or cosines of multiples of x, a problem which he embodied in his Théorie analytique de la chaleur (1822). Euler had already given the formulas for determining...

Retrieved 2010-04-26. Grothendieck, Alexander. "La Longue Marche à Travers la Théorie de Galois" (PDF). Archived from the original (PDF) on 2022-05-20. Retrieved...

powers in the summatory function of the power tower". Journal de Théorie des Nombres de Bordeaux. 22 (3): 703–718. doi:10.5802/jtnb.740. MR 2769339. Graham...

Hine, Mervyn (January 2003). "Working with Viki at CERN". CERN Courier. Kummer, Wolfgang (June 2002). "Victor Weisskopf: looking back on a distinguished...

function, and can also be expressed as a confluent hypergeometric function (Kummer's function): erf ⁡ x = 2 x π M ( 1 2 , 3 2 , − x 2 ) . {\displaystyle \operatorname...

C must be zero. Example: consider the following differential equation (Kummer's equation with a = 1 and b = 2): z u ″ + ( 2 − z ) u ′ − u = 0 {\displaystyle...

doi:10.1007/BF02419020 Picard, E. (1889), "Mémoire sur la théorie des fonctions algébriques de deux variables" (PDF), J. Math. Pures Appl., 5: 135–319 Rozov...

compact, connected Lie group. L. Schwartz (1983), "K-théorie et homotopie stable", Thesis, Université de Paris–VII Explicit description of K 0 ( B U ( n )...

Etale cohomology. Ch IV Knus, Max-Albert; Ojanguren, Manuel (1974), Théorie de la descente et algèbres d'Azumaya, Lecture Notes in Mathematics, vol. 389...