Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 32, 2007, 317-340

UNDECIDABLE PROPOSITIONS BY ODE'S

Peter Buser and Bruno Scarpellini

Ecole Polytechnique Fédérale de Lausanne, Section de Mathématiques
IGAT, SB, GEOM, station 8, CH-1015 Lausanne, Switzerland

Universität Basel, Departement Mathematik
4051 Basel, Rheinsprung 21, Switzerland

Abstract. Starting with elementary functions, we generate new functions by multiplication, integration and by solving ODE's so as to obtain a family M of real holomorphic functions such that: (*) if E \subseteq N is recursively enumerable then there is f \in M such that n \in E iff \int^{+\pi}_{-\pi} f(x)e^-inx dx \neq 0. Constructive aspects and relations to hypercomputation are discussed.

Key words: Recursively enumerable sets, theta functions, ordinary differential equations, hypercomputation.

Reference to this article: P. Buser and B. Scarpellini: Undecidable propositions by ODE's. Ann. Acad. Sci. Fenn. Math. 32 (2007), 317-340.

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