Number Theory and Its Applications (Lecture Notes in Pure and Applied Mathematics, Vol. 204)

"Addresses contemporary developments in number theory and coding theory, originally presented as lectures at summer school held at Bilkent University, Ankara, Turkey. Includes many results in book form for the first time." Number Theory and Its Applications provides up-to-date surveys on modular forms and Hecke operators, exponential sums, and sieve methods with applications to additive and multiplicative number theory, for example, the ideas behind the recent surprising proof that there are infinitely many primes of the form a[superscript 2] + b[superscript 4] are laid out ... contains numerous results on character sums and finite fields with applications to coding theory ... covers classical and new material on algebraic numbers, transcendence theory, and diophantine approximation, including the recent proof of algebraic independence of the numbers [pi], e[superscript x], [Gamma](1/4) ... dwells on the connections between the distribution of primes and the Riemann zeta-function ... and more. With nearly 1500 references, equations, drawings, and tables, Number Theory and Its Applications especially benefits number theorists, coding theorists, algebraists, algebraic geometers, applied mathematicians, information theorists, and upper-level undergraduate and graduate students in these fields This valuable reference addresses the methods leading to contemporary developments in number theory and coding theory, originally presented as lectures at a summer school held at Bilkent University, Ankara, Turkey. In this work, based on the cyclotomic theory of Carlitz and Hayes, we introduce a new kind of arithmetic progression for a rational function field k over a finite field.