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      On Toric Orbits in the Affine Sieve

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          Abstract

          We give a detailed analysis of a heuristic model for the failure of "saturation" in instances of the Affine Sieve having toral Zariski closure. Based on this model, we formulate precise conjectures on several classical problems of arithmetic interest, and test these against empirical data.

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          Levels of Distribution and the Affine Sieve

          Alex Kontorovich (2014)
          This article is an expanded version of the author's lecture in the Basic Notions Seminar at Harvard, September 2013. Our goal is a brief and introductory exposition of aspects of two topics in sieve theory which have received attention recently: (1) the spectacular work of Yitang Zhang, under the title "Level of Distribution," and (2) the so-called "Affine Sieve," introduced by Bourgain-Gamburd-Sarnak.
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            Sur la distribution des nombres entiers ayant une quantité fixée de facteurs premiers

            Jean Nicolas (1984)
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              On Fibonacci numbers with few prime divisors

              Yann Bugeaud, Florian Luca, Maurice Mignotte … (2005)
              Article 0 comments Cited 1 times – based on 0 reviews     Review now
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                Author and article information

                Journal
                Publication date Created: 09 August 2018
                Article
                ArXiV ID: 1808.03235
                SO-VID: 54dfe000-e96a-467c-9fde-9d172586a180
                License:

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                ACM classes 11B39, 11D09, 11J70, 11N37, 11N35
                Comments 20 pages, 6 figures
                Categories math.NT

                ScienceOpen disciplines: Number theory
                Data availability:
                ScienceOpen disciplines: Number theory

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