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 ?
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.
distinguished for his many fundamental contributions in algebraic number theory, arithmetic geometry and related areas in algebraic geometry), the Serre-Tate theorem in algebraic geometry, says that under certain conditions an abelian scheme (an projective algebraic variety that is also an algebraic group, i.
His mathematical interests are Algebraic Number Theory, Algebraic Geometry and Elliptic Curves and Modular Forms.
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.
Gauss' composition law offered a new way of thinking about relationships among numbers and led to the development of the mathematical field now known as algebraic number theory.
Cohen, A Course in Computational Algebraic Number Theory, Graduate Texts in Mathematics 138, Springer-Verlag, Berlin, 1996.
which he earned last year, Bhargava extended some work of the legendary 19th-century German mathematician Carl Friedrich Gauss, work that forms the basis of modern algebraic number theory.
Among their topics are designs, introducing difference sets, multipliers, necessary group conditions, representation theory, using algebraic number theory, and applications.
This mathematics textbook for graduate students covers the fundamentals of abstract algebra including fields and Galois theory, algebraic number theory, algebraic geometry and groups, rings and modules.
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).
For example, he describes how Fermat's last theorem, first posited in the year 1630, remained unsolved until Andrew Wiles published his solution in 1995 while also explaining how work on Fermat's theorem led to the development of algebraic number theory and complex analysis.