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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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The classical umbral calculus and the flow of a Drinfeld module
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by Nguyen Ngoc Dong Quan PDF
Trans. Amer. Math. Soc. 369 (2017), 1265-1289 Request permission

Abstract:

David Goss developed a very general Fourier transform in additive harmonic analysis in the function field setting. In order to introduce the Fourier transform for continuous characteristic $p$-valued functions on $\mathbb {Z}_p$, Goss introduced and studied an analogue of flows in finite characteristic. In this paper, we use another approach to study flows in finite characteristic. We recast the notion of a flow in the language of the classical umbral calculus, which allows us to generalize the formula for flows first proved by Goss to a more general setting. We study duality between flows using the classical umbral calculus, and show that the duality notion introduced by Goss seems to be a natural one. We also formulate a question of Goss about the exact relationship between two flows of a Drinfeld module in the language of the classical umbral calculus, and give a partial answer to it.
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Additional Information
  • Nguyen Ngoc Dong Quan
  • Affiliation: Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712
  • Address at time of publication: Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana 46556
  • Email: dongquan.ngoc.nguyen@gmail.com, dongquan.ngoc.nguyen@nd.edu
  • Received by editor(s): July 3, 2014
  • Received by editor(s) in revised form: May 25, 2015
  • Published electronically: September 27, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 369 (2017), 1265-1289
  • MSC (2010): Primary 05A40, 11G09
  • DOI: https://doi.org/10.1090/tran/6763
  • MathSciNet review: 3572273