Hilberth’s Theorem 94 and Function Fields

Howard Kleiman ()

Chapter 17 in Number Theory: New York Seminar 1991–1995, 1996, pp 221-228 from Springer

Abstract: Abstract Let f(x,y) be a monic absolutely irreducible polynomial in x of degree n with coefficients in Z[y]. If α is a root of f(x,y), L = Q(y)(α)/Q(y). Hilbert’s Theorem 94 [4] gives a procedure for determining rational primes p which divide the class number of a number field. Here an analogue of it is given for ordinary arithmetic function fields like L as defined by E. Weiss in [7]. A corollary of Theorem 1 is used to obtain rational prime divisors of class numbers of number fields L’ obtained from L by specialization of y into Z. Although the proof essentially follows that of Hilbert, use is made of the concept of NTU#x2019;s (non-trivial units) in fields like L. These units were implicity defined in [5].

Date: 1996
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DOI: 10.1007/978-1-4612-2418-1_17

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