Diophantine Undecidability of Holomorphy Rings of Function Fields of Characteristic
نویسنده
چکیده
Let K be a one-variable function field over a field of constants of characteristic 0. Let R be a holomorphy subring of K, not equal to K. We prove the following undecidability results for R: If K is recursive, then Hilbert’s Tenth Problem is undecidable in R. In general, there exist x1, . . . , xn ∈ R such that there is no algorithm to tell whether a polynomial equation with coefficients in Q(x1, . . . , xn) has solutions in R.
منابع مشابه
Diophantine Undecidability of Holomorphy Rings of Function Fields of Characteristic 0 Laurent Moret-bailly and Alexandra Shlapentokh
Let K be a one-variable function field over a field of constants of characteristic 0. Let R be a holomorphy subring of K, not equal to K. We prove the following undecidability results for R: If K is recursive, then Hilbert’s Tenth Problem is undecidable in R. In general, there exist x1, . . . , xn ∈ R such that there is no algorithm to tell whether a polynomial equation with coefficients in Q(x...
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— Let K be a one-variable function field over a field of constants of characteristic 0. Let R be a holomorphy subring of K, not equal to K. We prove the following undecidability results for R: if K is recursive, then Hilbert’s Tenth Problem is undecidable in R. In general, there exist x1, . . . , xn ∈ R such that there is no algorithm to tell whether a polynomial equation with coefficients in Q...
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