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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 |

Files in This Item:

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PUTheses2015-Nogues_Isabelle_Emmanuella.pdf | 425.28 kB | Adobe PDF | Request a copy |

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