Hilbert's Tenth Problem

By Alexandra Shlapentokh. Notices of the American Mathematical Society, 2006

67 citations recorded by the source corpus.

1. Introduction 2. Diophantine classes: definition and basic facts 3. Diophantine equivalence and diophantine decidability 4. Integrality at finitely many primes and divisibility of order at infinitely many primes 5. Bound equations for number fields and their consequences 6. Units of rings of W-integers of norm 1 7. Diophantine classes over number fields 8. Diophantine undecidability of function fields 9. Bounds for function fields 10. Diophantine classes over function fields 11. Mazur's conjectures and their consequences 12. Results of Poonen 13. Beyond global fields A. Recursion theory B. Number theory Bibliography Index.

Subfields: Algebra and Number Theory, Theoretical Computer Science

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