Elena Fuchs

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All published works

Action	Title	Year	Authors
+ PDF Chat	Prime and thickened prime components in Apollonian circle packings	2024	Holley Friedlander Elena Fuchs P. Harris Catherine Hsu James Rickards Katherine Sanden Damaris Schindler Katherine E. Stange
+	Connectivity of Markoff mod-p graphs and maximal divisors	2023	Jillian Eddy Elena Fuchs Matthew Litman Daniel M. Martin Nico Tripeny
+	Bounding Lifts of Markoff Triples mod $p$	2023	Elisa Bellah Siran Chen Elena Fuchs Lynnelle Ye
+	Orbits on K3 Surfaces of Markoff Type	2022	Elena Fuchs Matthew Litman Joseph H. Silverman Austin Tran
+	A Cryptographic Hash Function from Markoff Triples	2021	Elena Fuchs Kristin Lauter Matthew Litman Austin Tran
+	A Cryptographic Hash Function from Markoff Triples.	2021	Elena Fuchs Kristin Lauter Matthew Litman Austin Tran
+	A Cryptographic Hash Function from Markoff Triples	2021	Elena Fuchs Kristin Lauter Matthew Litman Austin Tran
+ PDF	On the 80th Birthday of Dmitry Borisovich Fuchs	2020	Alice Fialowski Ekaterina Fuchs Elena Fuchs Boris Khesin A. A. Kirillov Fedor Malikov Valentin Ovsienko Alexei Sossinsky Serge Tabachnikov
+ PDF	On the 80th Birthday of Dmitry Borisovich Fuchs	2020	Valentin Ovsienko Alice Fialowski Ekaterina Fuchs Elena Fuchs Boris Khesin A. A. Kirillov Fedor Malikov Alexei Sossinsky Serge Tabachnikov
+ PDF Chat	Local-global principles in circle packings	2019	Elena Fuchs Katherine E. Stange Xin Zhang
+	The dynamics of Super-Apollonian continued fractions	2018	Sneha Chaubey Elena Fuchs Robert Hines Katherine E. Stange
+	The Dynamics of Super-Apollonian Continued Fractions	2017	Sneha Chaubey Elena Fuchs Robert Hines Katherine E. Stange
+	The Dynamics of Super-Apollonian Continued Fractions	2017	Sneha Chaubey Elena Fuchs Robert H Hines Katherine E. Stange
+ PDF	Generic Thinness in Finitely Generated Subgroups of SL$_n(\mathbb Z)$	2016	Elena Fuchs Igor Rivin
+	Generic thinness in finitely generated subgroups of $\textrm{SL}_n(\mathbb Z)$	2015	Elena Fuchs Igor Rivin
+ PDF	Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions	2014	Elena Fuchs Chen Meiri Peter Sarnak
+	Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions	2013	Elena Fuchs Chen Meiri Peter Sarnak
+ PDF	Counting problems in Apollonian packings	2013	Elena Fuchs
+	Hyperbolic monodromy groups for the hypergeometric equation and Cartan involutions	2013	Elena Fuchs Chen Meiri Peter Sarnak
+ PDF Chat	On Representation of Integers by Binary Quadratic Forms	2012	Jean Bourgain Elena Fuchs
+ PDF	Some Experiments with Integral Apollonian Circle Packings	2011	Elena Fuchs Katherine Sanden
+	Strong approximation in the Apollonian group	2011	Elena Fuchs
+	A proof of the positive density conjecture for integer Apollonian circle packings	2011	Jean Bourgain Elena Fuchs
+	On representation of integers by binary quadratic forms	2011	Jean Bourgain Elena Fuchs
+	A proof of the positive density conjecture for integer Apollonian circle packings	2010	Jean Bourgain Elena Fuchs
+	Some experiments with integral Apollonian circle packings	2010	Elena Fuchs Katherine Sanden
+	Some experiments with integral Apollonian circle packings	2010	Elena Fuchs Katherine Sanden
+	A proof of the positive density conjecture for integer Apollonian circle packings	2010	Jean Bourgain Elena Fuchs
+ PDF	Longest Induced Cycles in Circulant Graphs	2005	Elena Fuchs
+	Longest Induced Cycles on Cayley Graphs	2004	Elena Fuchs Justin Sinz

Common Coauthors

Coauthor	Papers Together
Katherine E. Stange	5
Jean Bourgain	5
Matthew Litman	5
Katherine Sanden	4
Austin Tran	4
Sneha Chaubey	3
Chen Meiri	3
Peter Sarnak	3
Kristin Lauter	3
Boris Khesin	2
A. A. Kirillov	2
Robert Hines	2
Serge Tabachnikov	2
Fedor Malikov	2
Alice Fialowski	2
Valentin Ovsienko	2
Igor Rivin	2
Ekaterina Fuchs	2
Catherine Hsu	1
Justin Sinz	1
James Rickards	1
Daniel M. Martin	1
P. Harris	1
Holley Friedlander	1
Elisa Bellah	1
Damaris Schindler	1
Robert H Hines	1
Lynnelle Ye	1
Siran Chen	1
Jillian Eddy	1
Joseph H. Silverman	1
Xin Zhang	1
Alexei Sossinsky	1
Alexei Sossinsky	1
Nico Tripeny	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	Apollonian circle packings: number theory	2003	Ronald Graham Jeffrey C. Lagarias Colin L. Mallows Allan R. Wilks Catherine H. Yan	9
+	Rational Quadratic Forms	1982	J. W. S. Cassels	7
+	Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds	2011	Alex Kontorovich Hee Oh	6
+ PDF	The Apollonian Packing of Circles	1943	Edward Kasner Fred Supnick	5
+	Groups Acting on Hyperbolic Space	1998	Jürgen Elstrodt Fritz Grunewald J. Mennicke	5
+	A proof of the positive density conjecture for integer Apollonian circle packings	2011	Jean Bourgain Elena Fuchs	5
+	Estimates for representation numbers of quadratic forms	2006	Valentin Blomer Andrew Granville	5
+ PDF	Counting problems in Apollonian packings	2013	Elena Fuchs	4
+ PDF	Affine linear sieve, expanders, and sum-product	2009	Jean Bourgain Alex Gamburd Peter Sarnak	4
+ PDF Chat	Arithmeticity of certain symplectic hypergeometric groups	2014	Sandip Singh T. N. Venkataramana	4
+	Strong approximation in the Apollonian group	2011	Elena Fuchs	4
+ PDF	Some Experiments with Integral Apollonian Circle Packings	2011	Elena Fuchs Katherine Sanden	4
+ PDF	Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group	2005	Ronald Graham Jeffrey C. Lagarias Colin L. Mallows Allan R. Wilks Catherine H. Yan	4
+ PDF	From Apollonius to Zaremba: Local-global phenomena in thin orbits	2013	Alex Kontorovich	4
+	The Asymptotic Distribution of Lattice Points in Euclidean and Non-Euclidean Spaces	1982	Peter D. Lax Ralph S. Phillips	3
+	The Apollonian structure of Bianchi groups	2016	Katherine E. Stange	3
+	Representation of integers by positive ternary quadratic forms and equidistribution of lattice points on ellipsoids	1990	William Duke Rainer Schulze‐Pillot	3
+	Über die Darstellung von positiven, ganzen Zahlen durch die primitiven, binären quadratischen Formen einer nicht-quadratischen Diskriminante	1912	Paul Bernays	3
+	Abelian l-Adic Representations and Elliptic Curves	1997	Jean-Pierre Serre	3
+	An Absolute Property of Four Mutually Tangent Circles	2006	H. S. M. Coxeter	3
+ PDF Chat	Random subgroups of linear groups are free	2011	Richard Aoun	3
+	Analytic Number Theory	2004	Henryk Iwaniec Emmanuel Kowalski	3
+ PDF	Density of integer points on affine homogeneous varieties	1993	William Duke Zeév Rudnick Peter Sarnak	3
+ PDF	On sums of three squares	2003	James Cogdell	3
+	Discrete Subgroups of Semisimple Lie Groups	1991	Gregori Aleksandrovitch Margulis	3
+ PDF Chat	Beyond the Descartes Circle Theorem	2002	Jeffrey C. Lagarias Colin L. Mallows Allan R. Wilks	2
+	On the spectral gap for infinite index “congruence” subgroups of SL2(Z)	2002	Alex Gamburd	2
+	The Pythagorean Tree: A New Species	2008	H. Lee Price	2
+ PDF	A new form of the circle method, and its application to quadratic forms.	1996	D. R. Heath‐Brown	2
+	Elementary Methods in Analytic Number Theory.	1967	L. Carlitz А. О. Гелъфонд Yu. V. Linnik L. J. Mordell	2
+	Strong Approximation for Zariski-dense Subgroups of Semi-Simple Algebraic Groups	1984	Boris Weisfeiler	2
+ PDF	Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings	2005	Ronald Graham Jeffrey C. Lagarias Colin L. Mallows Allan R. Wilks Catherine H. Yan	2
+ PDF	The dynamics of Pythagorean Triples	2008	Dan Romik	2
+ PDF	Integral Apollonian Packings	2011	Peter Sarnak	2
+	ON GROUPS OF UNIT ELEMENTS OF CERTAIN QUADRATIC FORMS	1972	É. B. Vinberg	2
+ PDF	Mixing, counting, and equidistribution in Lie groups	1993	Alex Eskin Curt McMullen	2
+	Ergodic Theory: with a view towards Number Theory	2011	Manfred Einsiedler Thomas Ward	2
+ PDF	Hausdorff dimension and conformal dynamics, III: Computation of dimension	1998	Curtis T. McMullen	2
+	Diophantine Approximation On Bianchi Groups	1995	L. Ya. Vulakh	2
+	Elementary Number Theory, Group Theory and Ramanujan Graphs	2001	Giuliana P. Davidoff Peter Sarnak Alain Valette	2
+ PDF	The sequence of radii of the Apollonian packing	1982	David W. Boyd	2
+	Notes on Thin Matrix Groups	2012	Peter Sarnak	2
+	p-adic cycles	1969	Bernard Dwork	2
+ PDF Chat	Walks on groups, counting reducible matrices, polynomials, and surface and free group automorphisms	2008	Igor Rivin	2
+ PDF	The density of integer points on homogeneous varieties	1985	Wolfgang M. Schmidt	2
+	A Version of the Circle Method for the Representation of Integers by Quadratic Forms	2009	Nic Niedermowwe	2
+	On Representations of Integers in Thin Subgroups of $${{\rm SL}_2({\mathbb {Z}})}$$	2010	Jean Bourgain Alex Kontorovich	2
+	Integer Ratios of Factorials, Hypergeometric Functions, and Related Step Functions.	2009	Jonathan Bober	2
+	Ergodic theory for complex continued fractions	1982	Asmus L. Schmidt	2
+	A New Application of the Hardy-Littlewood-Kloosterman Method	1962	T. Estermann	2