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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A formal Mellin transform in the arithmetic of function fields


Author: David Goss
Journal: Trans. Amer. Math. Soc. 327 (1991), 567-582
MSC: Primary 11R58; Secondary 11S80, 11T55
MathSciNet review: 1041048
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Abstract: The Mellin transform is a fundamental tool of classical arithmetic. We would also like such a tool in the arithmetic of function fields based on Drinfeld modules, although a construction has not yet been found. One formal approach to finding Mellin transforms in classical theory is through $ p$-adic measures. It turns out that this approach also works for function fields. Thus this paper is devoted to exploring what can be learned this way. We will establish some very enticing connections with gamma functions and the Kummer-Vandiver conjecture for function fields.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1041048-5
PII: S 0002-9947(1991)1041048-5
Keywords: Mellin transforms, nonarchimedean measures, divided power series, hyper-derivatives, zeta functions, gamma functions, magic numbers
Article copyright: © Copyright 1991 American Mathematical Society