scientific article; zbMATH DE number 1821364

DOI10.1155/S107379280320516XzbMath1107.11049OpenAlexW1838580717MaRDI QIDQ4779941

Alexandra Shlapentokh

Publication date: 29 October 2002

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/s107379280320516x

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zbMATH Keywords

rational pointDiophantine equationDiophantine model

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Rational points (14G05) Diophantine equations (11D99)

Related Items (11)

Diophantine definability and decidability in extensions of degree 2 of totally real fields ⋮ On Diophantine definability and decidability in some infinite totally real extensions of ℚ ⋮ Elliptic curves retaining their rank in finite extensions and Hilbert's Tenth Problem for rings of algebraic numbers ⋮ Diophantine undecidability for some function fields of infinite transcendence degree and positive characteristic ⋮ Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of $\mathbb {Q}$ ⋮ Rings of algebraic numbers in infinite extensions of \(\mathbb Q\) and elliptic curves retaining their rank ⋮ What can and cannot be done with Diophantine problems ⋮ Descent on elliptic curves and Hilbert’s tenth problem ⋮ Julia Robinson numbers ⋮ Diophantine undecidability of holomorphy rings of function fields of characteristic 0 ⋮ First-order definitions of rational functions and \({\mathcal S}\)-integers over holomorphy rings of algebraic functions of characteristic 0

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