A note on global units and local units of function fields
نویسندگان
چکیده
منابع مشابه
Maximal independent systems of units in global function fields
Introduction. Around 1980, Galovich and Rosen (cf. [GR1] and [GR2]) computed the index of cyclotomic units in the full group of units in a cyclotomic function field over a rational function field over a finite field. Later, Hayes [H1] and Oukhaba [O] obtained a few index formulae of the elliptic units in some special extensions of the global function fields with some restrictions on the infinit...
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چکیده ندارد.
15 صفحه اولThe Sum of Two S-units Being a Perfect Power in Global Function Fields
Let x1 and x2 be integers divisible only by some fixed primes. Is it possible that x1 + x2 is a perfect power? Special cases of the equation x1 +x2 = yk were formerly considered over Z. In this paper we develop an algorithm to solve this equation over global algebraic function fields. Our method is illustrated by two explicit examples.
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In 2007, Jarden and Narkiewicz raised the following question: Is it true that each algebraic number field has a finite extension L such that the ring of integers of L is generated by its units (as a ring)? In this article, we answer the analogous question in the function field case. More precisely, it is shown that for every finite non-empty set S of places of an algebraic function field F |K o...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2009
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa139-1-1