Carlitz-Kummer function fields
β Scribed by Fred Schultheis
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 642 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this article, we prove Wiles and Coates Wiles explicit reciprocity laws for the local symbols attached to cyclotomic functions fields.
Let [, k ] n k=0 , n<m, be a family of polynomials orthogonal with respect to the positive semi-definite bilinear form x j :=&1+(2j&1)Γm. These polynomials are known as Gram polynomials. The present paper investigates the growth of |, k (x)| as a function of k and m for fixed x # [&1, 1]. We show t
In this article, we show that a value of the Carlitz Goss gamma function for the ring F q [X] is transcendental over the field F q (X) if and only if the argument is not an element of N=[0, 1, 2, . . .]. We also answer a question of J.-P. Allouche, and we show the transcendence of monomials built on
We compare several properties and constructions of the Carlitz polynomials and digit derivatives for continuous functions on F q [[T]]. In particular, we show a close relation between them as orthonormal bases. Moreover, parallel to Carlitz's coefficient formula, we give the closed formula for the e