Computational number theory

In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry.Computational number theory has applications to cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the modularity conjecture, the Sato-Tate conjecture, and explicit aspects of the Langlands program.

Comment
enIn mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry.Computational number theory has applications to cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the modularity conjecture, the Sato-Tate conjecture, and explicit aspects of the Langlands program.
Has abstract
enIn mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating and solving problems in number theory and arithmetic geometry, including algorithms for primality testing and integer factorization, finding solutions to diophantine equations, and explicit methods in arithmetic geometry.Computational number theory has applications to cryptography, including RSA, elliptic curve cryptography and post-quantum cryptography, and is used to investigate conjectures and open problems in number theory, including the Riemann hypothesis, the Birch and Swinnerton-Dyer conjecture, the ABC conjecture, the modularity conjecture, the Sato-Tate conjecture, and explicit aspects of the Langlands program.
Hypernym
Study
Is primary topic of
Computational number theory
Label
enComputational number theory
Link from a Wikipage to an external page
www.cambridge.org/us/academic/subjects/mathematics/number-theory/algorithmic-number-theory-lattices-number-fields-curves-and-cryptography%3Fformat=HB&isbn=9780521808545
cs.uwaterloo.ca/~shallit/ant.html
archive.org/details/factorizationpri0000bres
www.ams.org/bookpages/stml-68
Link from a Wikipage to another Wikipage
ABC conjecture
Arithmetic geometry
Birch and Swinnerton-Dyer conjecture
Cambridge University Press
Category:Computational fields of study
Category:Computational number theory
Category:Number theory
Computation
Computer science
Conjectures
Cryptography
Diophantine equations
Elliptic curve cryptography
Fast Library for Number Theory
GP
Graduate Texts in Mathematics
Integer factorization
Langlands program
Magma computer algebra system
Mathematics
Modularity theorem
Number theory
Number Theory Library
Open problems
Post-quantum cryptography
Primality testing
Riemann hypothesis
RSA (cryptosystem)
SageMath
Sato-Tate conjecture
Springer-Verlag
SameAs
2UxUu
Algorithmische Zahlentheorie
Algoritmisk talteori
Algorytmiczna teoria liczb
Computational number theory
Lý thuyết số tính toán
m.02k2hy
Q2646614
Teoria computacional dos números
Teoria computazionale dei numeri
Teoría de números computacional
Théorie algorithmique des nombres
Алгоритмічна теорія чисел
תורת המספרים החישובית
نظرية الأعداد الحاسوبية
نظریه اعداد رایانشی
計算数論
计算数论
Subject
Category:Computational fields of study
Category:Computational number theory
Category:Number theory
WasDerivedFrom
Computational number theory?oldid=1020367815&ns=0
WikiPageLength
6345
Wikipage page ID
511466
Wikipage revision ID
1020367815
WikiPageUsesTemplate
Template:Algebraic curves navbox
Template:Cite book
Template:Commonscatinline
Template:Number-theoretic algorithms
Template:Number theory-footer
Template:R
Template:Reflist
Template:Short description