Case studies of Experimental Mathematics: padic valuations of recurrences

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Title 
Case studies of Experimental Mathematics: padic valuations of recurrences 
Author 
Medina, Luis A 
School 
School of Science and Engineering 
Academic Field 
Mathematics 
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 tn=Pnt n1, 0.0.1 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 padic 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 Z/pZ and the growth of the padic valuation is presented Finally, in the last chapter a relation between Dirichlet Series and the evaluation of a class of logarithmic integrals is studied 
Language 
eng 
Advisor(s) 
Moll, Victor H 
Degree Date 
2008 
Degree 
Ph.D 
Publisher 
Tulane University 
Publication Date 
2008 
Source 
Source: 142 p., Dissertation Abstracts International, Volume: 6903, Section: B, page: 1688 
Identifier 
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Rights 
Copyright is in accordance with U.S. Copyright law 
Contact Information 
acase@tulane.edu 
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