We show that Diophantine problem (otherwise known as Hilbert's Tenth Problem) is undecidable over the fields of algebraic functions over the finite fields of constants of characteristic greater than two. This is the first example of Diophantine undecidability over any algebraic field. We also show t
Places of degree one in function fields over finite fields
β Scribed by Joseph Lewittes
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 439 KB
- Volume
- 69
- Category
- Article
- ISSN
- 0022-4049
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π SIMILAR VOLUMES
For a tower F 1 Κ F 2 Κ ΠΈ ΠΈ ΠΈ of algebraic function fields F i β«ή/β¬ q , define Ο lim iΗΘ N(F i )/g(F i ), where N(F i ) is the number of rational places and g(F i ) is the genus of F i β«ή/β¬ q . The tower is said to be asymptotically good if ΟΎ 0. We give a very simple explicit example of an asymptoti
Let gn denote the iterates of a function y from the finite field FG into itself, defined induct~ively by go@) = x and g"(x) = g ( g n -l ( x ) ) , n>O. We study the existence of solutions to the functional equation g"=f, where f is a given linear, quadratic or CHEBYSIIEV function on .Fq, \*) Researc