Dubickas, On the degree of a linear form in conjugates of an algebraic number
, Illinois J.
Prerequisites are algebraic geometry, algebraic number
theory, and some group cohomology.
Particularly, we bring symmetries, computational- and complexity theoretic aspects, and connections with algebraic number
theory, -geometry, and -combinatorics into play in novel ways.
Neukirch Algebraic Number
Theory Springer- Verlag Inc.
Akiyama, Cubic Pisot units with finite beta expansions, Algebraic Number
Theory and Diophantine Analysis, (2000), pp.
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.
Our main results (Theorem 5 and Proposition 7) may seem surprising as we might expect that any algebraic number
would be computable in our setting.
Let a, b, c > 0 and u be a real algebraic number
Stan, Florin, University of Illinois, Urbana-Champaign, Trace problems in algebraic number
fields and applications to characters of finite groups.
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.
In these cases, [rho] is an algebraic number
of degree 2 (e.