algebraic number theory


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algebraic number theory

[¦al·jə¦brā·ik ′nəm·bər ‚thē·ə·rē]
(mathematics)
The study of properties of real numbers, especially integers, using the methods of abstract algebra.
References in periodicals archive ?
Ten talks delivered at the June 2017 conference held in Marseille, France explore algebraic number theory, Diophantine geometry, curves and abelian varieties over finite fields, and applications in codes and cryptography.
The Institute for Advanced Study said he works"at the intersection of analytic number theory, algebraic number theory, and representation theory."
Neukirch, Algebraic number theory, translated from the 1992 German original and with a note by Norbert Schappacher, Grundlehren der Mathematischen Wissenschaften, 322, Springer, Berlin, 1999.
Neukirch Algebraic Number Theory Springer- Verlag Inc.
Eleven contributions are selected from the eight working groups in the areas of elliptic surfaces and the Mahler measure, analytic number theory, number theory in functions fields and algebraic geometry over finite fields, arithmetic algebraic geometry, K-theory and algebraic number theory, arithmetic geometry, modular forms, and arithmetic intersection theory.
Proved by the work of French mathematician Jean-Pierre Serre (who has made fundamental contributions to algebraic topology, algebraic geometry, and algebraic number theory) and American mathematician John Torrence Tate, Jr.
Ten chapters cover algebraic number theory and quadratic fields; ideal theory; binary quadratic forms; Diophantine approximation; arithmetic functions; p-adic analysis; Dirichlet characters, density, and primes in progression; applications to Diophantine equations; elliptic curves; and modular forms.
Even more of a challenge to come to grips with the complexities of Pythagoras and algebraic number theory if your dad is out of work and the family diet is baked beans.
* Mathematicians reached a milestone in algebraic number theory by proving the local Langlands correspondence, a conjecture that concerns prime numbers and perfect squares (157: 47).
Prerequisites are algebraic geometry, algebraic number theory, and some group cohomology.
Tate, Fourier analysis in number fields, and Hecke's zeta-functions, in Algebraic Number Theory (Proc.

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