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
โฆ LIBER โฆ
The undecidability of fields of rational functions over fields of characteristic 2
โ Scribed by Yu. G. Penzin
- Publisher
- Springer US
- Year
- 1973
- Tongue
- English
- Weight
- 219 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0002-5232
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Diophantine Undecidability over Algebrai
โ
Alexandra Shlapentokh
๐
Article
๐
1996
๐
Elsevier Science
๐
English
โ 825 KB
Hilbert's Tenth Problem for fields of ra
โ
Thanases Pheidas
๐
Article
๐
1991
๐
Springer-Verlag
๐
English
โ 448 KB
Factorization of Trinomials over Galois
โ
Uzi Vishne
๐
Article
๐
1997
๐
Elsevier Science
๐
English
โ 200 KB
We study the parity of the number of irreducible factors of trinomials over Galois fields of characteristic 2. As a consequence, some sufficient conditions for a trinomial being reducible are obtained. For example, x n ฯฉ ax k ฯฉ b สฆ GF(2 t )[x] is reducible if both n, t are even, except possibly when
On the representation of groups over rat
โ
V. A. Churkin
๐
Article
๐
1968
๐
Springer US
๐
English
โ 138 KB
Supersingular Curves of Genus 2 over Fin
โ
Gerard Van Der Geer; Marcel Van Der Vlugt
๐
Article
๐
1992
๐
John Wiley and Sons
๐
English
โ 396 KB
Classification of Quadratic Forms over S
โ
Mohamed Abdou Elomary; Jean-Pierre Tignol
๐
Article
๐
2001
๐
Elsevier Science
๐
English
โ 188 KB
Quadratic forms over division algebras over local or global fields of characteristic 2 are classified by an invariant derived from the Clifford algebra construction.