30 relations: Algebraic closure, American Mathematical Society, Andrew Wiles, Annals of Mathematics, Barry Mazur, Bernoulli number, Class field theory, Codomain, Crelle's Journal, Cyclotomic field, Domain of a function, Galois module, Heinrich-Wolfgang Leopoldt, Inventiones Mathematicae, Kenkichi Iwasawa, Kummer's congruence, L-function, Main conjecture of Iwasawa theory, Mathematics, P-adic distribution, P-adic number, Prime number, Princeton University Press, Profinite group, Riemann zeta function, Special values of L-functions, Springer Science+Business Media, Teichmüller character, Tomio Kubota, Tower of fields.
In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed.
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
Sir Andrew John Wiles (born 11 April 1953) is a British mathematician and a Royal Society Research Professor at the University of Oxford, specialising in number theory.
The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study.
Barry Charles Mazur (born December 19, 1937) is an American mathematician and a Gerhard Gade University Professor at Harvard University.
In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory.
In mathematics, class field theory is a major branch of algebraic number theory that studies abelian extensions of local fields (one-dimensional local fields) and "global fields" (one-dimensional global fields) such as number fields and function fields of curves over finite fields in terms of abelian topological groups associated to the fields.
In mathematics, the codomain or target set of a function is the set into which all of the output of the function is constrained to fall.
Crelle's Journal, or just Crelle, is the common name for a mathematics journal, the Journal für die reine und angewandte Mathematik (in English: Journal for Pure and Applied Mathematics).
In number theory, a cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to, the field of rational numbers.
In mathematics, and more specifically in naive set theory, the domain of definition (or simply the domain) of a function is the set of "input" or argument values for which the function is defined.
In mathematics, a Galois module is a ''G''-module, with G being the Galois group of some extension of fields.
Heinrich-Wolfgang Leopoldt (22 August 1927 – 28 July 2011) was a German mathematician, who worked on algebraic number theory.
Inventiones Mathematicae is a mathematical journal published monthly by Springer Science+Business Media.
Kenkichi Iwasawa (岩澤 健吉 Iwasawa Kenkichi, September 11, 1917 – October 26, 1998) was a Japanese mathematician who is known for his influence on algebraic number theory.
In mathematics, Kummer's congruences are some congruences involving Bernoulli numbers, found by.
In mathematics, an L-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects.
In mathematics, the main conjecture of Iwasawa theory is a deep relationship between ''p''-adic ''L''-functions and ideal class groups of cyclotomic fields, proved by Kenkichi Iwasawa for primes satisfying the Kummer–Vandiver conjecture and proved for all primes by.
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
In mathematics, a p-adic distribution is an analogue of ordinary distributions (i.e. generalized functions) that takes values in a ring of ''p''-adic numbers.
In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.
A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
Princeton University Press is an independent publisher with close connections to Princeton University.
In mathematics, profinite groups are topological groups that are in a certain sense assembled from finite groups.
The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.
In mathematics, the study of special values of L-functions is a subfield of number theory devoted to generalising formulae such as the Leibniz formula for pi, namely by the recognition that expression on the left-hand side is also L(1) where L(s) is the Dirichlet L-function for the Gaussian field.
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
In number theory, the Teichmüller character ω (at a prime p) is a character of (Z/qZ)×, where q.
is a Japanese mathematician, who studies number theory.
In mathematics, a tower of fields is a sequence of field extensions The name comes from such sequences often being written in the form A tower of fields may be finite or infinite.