Wyniki wyszukiwania

1

Polynomial parametrizations of length 4 Büchi sequences

100%

Vidaux X.

Acta Arithmetica

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2011

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tom 150

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nr 3

209-226

2

Extensions of Büchi's problem: Questions of decidability for addition and kth powers

63%

Pheidas T., Vidaux X.

Fundamenta Mathematicae

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2005

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tom 185

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nr 2

171-194

EN

We generalize a question of Büchi: Let R be an integral domain, C a subring and k ≥ 2 an integer. Is there an algorithm to decide the solvability in R of any given system of polynomial equations, each of which is linear in the kth powers of the unknowns, with coefficients in C? We state a number-theoretical problem, depending on k, a positive answer to which would imply a negative answer to the question for R = C = ℤ. We reduce a negative answer for k = 2 and for R = F(t), the field of rational functions over a field of zero characteristic, to the undecidability of the ring theory of F(t). We address a similar question where we allow, along with the equations, also conditions of the form "x is a constant" and "x takes the value 0 at t = 0", for k = 3 and for function fields R = F(t) of zero characteristic, with C = ℤ[t]. We prove that a negative answer to this question would follow from a negative answer for a ring between ℤ and the extension of ℤ by a primitive cube root of 1.

3

A characterization of Büchi's integer sequences of length 3

63%

Sáez P., Vidaux X.

Acta Arithmetica

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2011

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tom 149

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nr 1

37-56

Ograniczanie wyników

2 Acta Arithmetica

1 Fundamenta Mathematicae

3 Vidaux X.

1 Pheidas T.

1 Sáez P.

2 2011

1 2005

Polynomial parametrizations of length 4 Büchi sequences

Extensions of Büchi's problem: Questions of decidability for addition and kth powers

A characterization of Büchi's integer sequences of length 3