The Affine Sieve Beyond Expansion I: Thin Hypotenuses

Jean Bourgain, Alex Kontorovich

Type: Preprint

Publication Date: 2013-01-01

Citations: 6

DOI: https://doi.org/10.48550/arxiv.1307.3535

View Publication

Locations

arXiv (Cornell University) - View
DataCite API - View

Similar Works

Action	Title	Year	Authors
+	The Affine Sieve Beyond Expansion I: Thin Hypotenuses: Fig. 1.	2014	Jean Bourgain Alex Kontorovich
+	A Friendly Intro to Sieves with a Look Towards Recent Progress on the Twin Primes Conjecture	2014	David Lowry-Duda
+	A Friendly Intro to Sieves with a Look Towards Recent Progress on the Twin Primes Conjecture	2014	David Lowry-Duda
+ PDF Chat	Combinatorics of Serre weights in the potentially Barsotti–Tate setting	2023	Xavier Caruso Ágnes Dávid Ariane Mézard
+ PDF Chat	Bounded gaps between primes in multidimensional Hecke equidistribution problems	2019	Jesse Thorner
+	A sieve problem over the Gaussian integers	2010	D. R. Heath‐Brown
+	A sieve problem over the Gaussian integers	2010	Waldemar Schlackow
+	Notes on Mitsui's Prime Number Theorem with Siegel zeros	2022	Wataru Kai
+	Bilinear forms and the large sieve	2019
+	Bilinear forms and the large sieve	2004	Henryk Iwaniec Emmanuel Kowalski
+	The case κ = 1: the linear sieve	2008	Harold G. Diamond H. Halberstam
+	Higher rank sieves and applications	2016	Akshaa Vatwani
+	Counting $S_5$-fields with a power saving error term	2013	Arul Shankar Jacob Tsimerman
+ PDF Chat	The Hyperbolic Sieve of Prime Numbers.	2023	Charles Kusniec
+	The Quadratic Sieve	2009	Gregory V. Bard
+ PDF Chat	A large sieve inequality of Elliott–Montgomery–Vaughan type for Maass forms on GL($n,\mathbb R$) with applications	2020	Yuk-Kam Lau Ming Ho Ng Emmanuel Royer Yingnan Wang
+	Constellations of gaps in Eratosthenes sieve	2015	Fred B. Holt
+	Primes with a missing digit: distribution in arithmetic progressions and an application in sieve theory	2021	Kunjakanan Nath
+	Large sieve inequality with sparse sets of moduli applied to Goldbach conjecture	2017	Claus Bauer
+	Large sieve inequality with sparse sets of moduli applied to Goldbach conjecture	2016	Claus Bauer

Works That Cite This (6)

Action	Title	Year	Authors
+	Almost Prime Coordinates for Anisotropic and Thin Pythagorean Orbits	2014	Jiuzu Hong Alex Kontorovich
+	Beyond Expansion II: Low-Lying Fundamental Geodesics	2014	Jean Bourgain Alex Kontorovich
+ PDF Chat	Beyond Expansion IV: Traces of Thin Semigroups	2018	Jean Bourgain Alex Kontorovich
+	Geometry and Arithmetic of Crystallographic Sphere Packings	2017	Alex Kontorovich Kei Nakamura
+	Effective equidistribution of shears and applications	2015	Dubi Kelmer Alex Kontorovich
+	Beyond Expansion IV: Traces of Thin Semigroups	2013	Jean Bourgain Alex Kontorovich

Works Cited by This (12)

Action	Title	Year	Authors
+ PDF Chat	The limit set of a Fuchsian group	1976	S. J. Patterson
+ PDF Chat	The hyperbolic lattice point count in infinite volume with applications to sieves	2009	Alex Kontorovich
+	Fields of large transcendence degree generated by values of elliptic functions	1983	David Masser G. Wüstholz
+	On Representations of Integers in Thin Subgroups of $${{\rm SL}_2({\mathbb {Z}})}$$	2010	Jean Bourgain Alex Kontorovich
+ PDF Chat	Affine linear sieve, expanders, and sum-product	2009	Jean Bourgain Alex Gamburd Peter Sarnak
+	Sieving and expanders⁎⁎The first author was supported in part by NSF grant DMS-0322370. The second author was supported in part by NSF grant DMS-0111298 and DMS-0501245. The third author was supported in part by Oscar Veblen Fund (IAS) and the NSF.	2006	Jean Bourgain Alex Gamburd Peter Sarnak
+	Zaremba’s conjecture	2019	Stephan Ramon Garcia Steven Miller
+	The Asymptotic Distribution of Lattice Points in Euclidean and Non-Euclidean Spaces	1982	Peter D. Lax Ralph S. Phillips
+	On the Local-Global Conjecture for integral Apollonian gaskets	2012	Jean Bourgain Alex Kontorovich
+ PDF Chat	Sector Estimates for Hyperbolic Isometries	2010	Jean Bourgain Alex Kontorovich Peter Sarnak