Case studies of Experimental Mathematics: p-adic valuations of recurrences

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" Case studies of Experimental Mathematics: p-adic valuations of recurrences "
Luis A. Medina V. H. Moll

Document Type	:	Latin Dissertation
Language of Document	:	English
Record Number	:	52881
Doc. No	:	TL22835
Call number	:	‭3306909‬
Main Entry	:	Luis A. Medina
Title & Author	:	Case studies of Experimental Mathematics: p-adic valuations of recurrences\ Luis A. Medina
College	:	Tulane University School of Science and Engineering
Date	:	2008
Degree	:	Ph.D.
student score	:	2008
Page No	:	142
Abstract	:	This work presents some instances of Experimental Mathematics in Number Theory. The arithmetical properties of an arctangent sum is explored, in particular, its connections to different mathematical objects are shown. One of this connections is the link between the sum and a sequence of type[special characters omitted] where P(x) is a polynomial with integer coefficients. These type of sequences arise in different types of problems like the integration of rational functions and the evaluation of infinite sums. The asymptotic behavior of the p-adic valuation for sequences of type (0.0.1) is described. In particular, the connection between the zeros of the polynomials P(x) in the finite field [special characters omitted] and the growth of the p-adic valuation is presented. Finally, in the last chapter a relation between Dirichlet Series and the evaluation of a class of logarithmic integrals is studied.
Subject	:	Pure sciences; Experimental mathematics; Recurrences; Valuations; p-adic; Mathematics; 0405:Mathematics
Added Entry	:	V. H. Moll
Added Entry	:	Tulane University School of Science and Engineering