Get it on Google Play
New! Download Unionpedia on your Android™ device!
Faster access than browser!

P-adic L-function

Index P-adic L-function

In mathematics, a p-adic zeta function, or more generally a p-adic L-function, is a function analogous to the Riemann zeta function, or more general ''L''-functions, but whose domain and target are p-adic (where p is a prime number). [1]

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.

Algebraic closure

In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed.

New!!: P-adic L-function and Algebraic closure · See more »

American Mathematical Society

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.

New!!: P-adic L-function and American Mathematical Society · See more »

Andrew Wiles

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.

New!!: P-adic L-function and Andrew Wiles · See more »

Annals of Mathematics

The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study.

New!!: P-adic L-function and Annals of Mathematics · See more »

Barry Mazur

Barry Charles Mazur (born December 19, 1937) is an American mathematician and a Gerhard Gade University Professor at Harvard University.

New!!: P-adic L-function and Barry Mazur · See more »

Bernoulli number

In mathematics, the Bernoulli numbers are a sequence of rational numbers which occur frequently in number theory.

New!!: P-adic L-function and Bernoulli number · See more »

Class field 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.

New!!: P-adic L-function and Class field theory · See more »


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.

New!!: P-adic L-function and Codomain · See more »

Crelle's Journal

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).

New!!: P-adic L-function and Crelle's Journal · See more »

Cyclotomic field

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.

New!!: P-adic L-function and Cyclotomic field · See more »

Domain of a function

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.

New!!: P-adic L-function and Domain of a function · See more »

Galois module

In mathematics, a Galois module is a ''G''-module, with G being the Galois group of some extension of fields.

New!!: P-adic L-function and Galois module · See more »

Heinrich-Wolfgang Leopoldt

Heinrich-Wolfgang Leopoldt (22 August 1927 – 28 July 2011) was a German mathematician, who worked on algebraic number theory.

New!!: P-adic L-function and Heinrich-Wolfgang Leopoldt · See more »

Inventiones Mathematicae

Inventiones Mathematicae is a mathematical journal published monthly by Springer Science+Business Media.

New!!: P-adic L-function and Inventiones Mathematicae · See more »

Kenkichi Iwasawa

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.

New!!: P-adic L-function and Kenkichi Iwasawa · See more »

Kummer's congruence

In mathematics, Kummer's congruences are some congruences involving Bernoulli numbers, found by.

New!!: P-adic L-function and Kummer's congruence · See more »


In mathematics, an L-function is a meromorphic function on the complex plane, associated to one out of several categories of mathematical objects.

New!!: P-adic L-function and L-function · See more »

Main conjecture of Iwasawa theory

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.

New!!: P-adic L-function and Main conjecture of Iwasawa theory · See more »


Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

New!!: P-adic L-function and Mathematics · See more »

P-adic distribution

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.

New!!: P-adic L-function and P-adic distribution · See more »

P-adic number

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.

New!!: P-adic L-function and P-adic number · See more »

Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

New!!: P-adic L-function and Prime number · See more »

Princeton University Press

Princeton University Press is an independent publisher with close connections to Princeton University.

New!!: P-adic L-function and Princeton University Press · See more »

Profinite group

In mathematics, profinite groups are topological groups that are in a certain sense assembled from finite groups.

New!!: P-adic L-function and Profinite group · See more »

Riemann zeta function

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.

New!!: P-adic L-function and Riemann zeta function · See more »

Special values of L-functions

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.

New!!: P-adic L-function and Special values of L-functions · See more »

Springer Science+Business Media

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.

New!!: P-adic L-function and Springer Science+Business Media · See more »

Teichmüller character

In number theory, the Teichmüller character ω (at a prime p) is a character of (Z/qZ)×, where q.

New!!: P-adic L-function and Teichmüller character · See more »

Tomio Kubota

is a Japanese mathematician, who studies number theory.

New!!: P-adic L-function and Tomio Kubota · See more »

Tower of fields

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.

New!!: P-adic L-function and Tower of fields · See more »

Redirects here:

Analytic p-adic L-function, Arithmetic p-adic L-function, P adic L function, P-adic L function, P-adic Riemann zeta function, P-adic zeta function.


[1] https://en.wikipedia.org/wiki/P-adic_L-function

Hey! We are on Facebook now! »