On Toric Orbits in the Affine Sieve

Alex Kontorovich, Jeffrey C. Lagarias

Type: Article

Publication Date: 2019-06-19

Citations: 3

DOI: https://doi.org/10.1080/10586458.2019.1616337

Abstract

We give a detailed analysis of a probabilistic 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.

Locations

Experimental Mathematics - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (8)

Action	Title	Year	Authors
+ PDF Chat	Sur la distribution des nombres entiers ayant une quantité fixée de facteurs premiers	1984	Jean Nicolas
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+ PDF Chat	Affine linear sieve, expanders, and sum-product	2009	Jean Bourgain Alex Gamburd Peter Sarnak
+ PDF Chat	American Mathematical Monthly	2010	Daniel J. Velleman
+ PDF Chat	On Fibonacci numbers with few prime divisors	2005	Yann Bugeaud Florian Luca Maurice Mignotte Samir Siksek
+	Baking a Pi with Factorials: 11333 [2007, 926].	2009	Jonathan Bober Jeffrey C. Lagarias Byron Schmuland
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