Israel Journal of Mathematics

, Volume 105, Issue 1, pp 323–335 | Cite as

Values of rational functions on non-hilbertian fields and a question of Weissauer

  • P. Corvaja
  • U. Zannier


We answer in the negative a question raised by Fried and Jarden, asking whether the quotient field of a unique factorization domain with infinitely many primes is necessarily hilbertian. This implies a negative answer to a related question of Weissauer. Our constructions are simple and take place inside the field of algebraic numbers. Simultaneously we investigate the relation of hilbertianity of a fieldK with the structure of the value sets of rational functions onK: we construct a non-hilbertian subfieldK of\(\bar {\mathbb{Q}}\) such that, given anyf 1 ,…,f h ∈K(x), each of degree ≥2, the union ∪ z=1 h f z(K) does not containK.


Rational Function Prime Ideal Galois Group Number Field Algebraic Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Hebrew University 1998

Authors and Affiliations

  1. 1.Dip. Mat. Inf.Università di UdineUdineItaly
  2. 2.Ist. Univ. Arch. D.C.A.VeneziaItaly

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