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Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01wh246v44x
Title: From automata theory to number theory: p-regularity of p-adic valuations of number theoretic sequences
Authors: Nogues, Isabelle Emmanuella
Advisors: Bhargava, Manjul
Contributors: Caraiani, Ana
Department: Mathematics
Class Year: 2015
Abstract: Let p be a prime, νp(x) the p-adic valuation of x, and {νp(f(n))}n≥0 a sequence in Qp generated by the function f : Zp → Qp. This paper examines the convergence properties of functions f(z) in Qp. We study the specific examples of linear recurrent sequences, generated by analytic p-adic functions, and the special factorial sequence of S ⊂ Z, {n!S}n≥0 defined by Bhargava. Here, S ⊂ Z is a union of congruence classes modulo p l. Instead of using standard analytic and algebraic arguments, we use the notion of p-regularity of {νp(f(n))}n≥0 to study the convergence properties of f(n) in Qp. To do so, we determine conditions on f(z) such that {νp(f(n))}n≥0 is p-regular.
Extent: 46 pages
URI: http://arks.princeton.edu/ark:/88435/dsp01wh246v44x
Type of Material: Princeton University Senior Theses
Language: en_US
Appears in Collections:Mathematics, 1934-2016

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