Mark E. Watkins

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All published works

Action	Title	Year	Authors
+ PDF Chat	Distribution of the 2-Selmer rank under twisting	2022	Mark E. Watkins
+	Comments on Deuring's zero-spacing phenomenon	2020	Mark E. Watkins
+ PDF Chat	Lobe, edge, and arc transitivity of graphs of connectivity 1	2019	Jack E. Graver Mark E. Watkins
+	CLASS NUMBER ONE FROM ANALYTIC RANK TWO	2019	Mark E. Watkins
+	Lobe, Edge, and Arc Transitivity of Graphs of Connectivity 1	2018	Jack E. Graver Mark E. Watkins
+	A spectral proof of class number one	2018	Mark E. Watkins
+ PDF Chat	Infinite Graphical Frobenius Representations	2018	Mark E. Watkins
+ PDF Chat	Jacobi sums and Grössencharacters	2018	Mark E. Watkins
+ PDF Chat	Graphical Frobenius representations	2018	John Kevin Doyle Thomas W. Tucker Mark E. Watkins
+	Lobe, Edge, and Arc Transitivity of Graphs of Connectivity 1	2018	Jack E. Graver Mark E. Watkins
+ PDF Chat	Growth of face-homogeneous tessellations	2017	Stephen J. Graves Mark E. Watkins
+	Growth of Face-Homogeneous Tessellations	2017	Stephen J. Graves Mark E. Watkins
+	Growth of Face-Homogeneous Tessellations	2017	Stephen J. Graves Mark E. Watkins
+ PDF Chat	Ranks of quadratic twists of elliptic curves	2015	Mark E. Watkins Stephen Robert Donnelly Noam D. Elkies Tom Fisher Andrew Granville Nicholas F. Rogers
+ PDF Chat	Infinite motion and 2-distinguishability of graphs and groups	2014	Wilfried Imrich Simon M. Smith Thomas W. Tucker Mark E. Watkins
+	Automorphisms	2013	Mark E. Watkins
+	Infinite Motion and 2-Distinguishability of Graphs and Groups	2013	Wilfried Imrich Simon M. Smith Thomas W. Tucker Mark E. Watkins
+	Bounding the distinguishing number of infinite graphs	2013	Simon M. Smith Mark E. Watkins
+	Bounding the distinguishing number of infinite graphs	2013	Simon Smith Mark E. Watkins
+	Infinite Motion and 2-Distinguishability of Graphs and Groups	2013	Wilfried Imrich Simon Smith Thomas W. Tucker Mark E. Watkins
+ PDF Chat	Distinguishability of Infinite Groups and Graphs	2012	Simon M. Smith Thomas W. Tucker Mark E. Watkins
+ PDF Chat	Imprimitivity of locally finite, 1-ended, planar graphs	2012	Jozef Širáň‬ Mark E. Watkins
+	Explicit methods in number theory. Rational points and Diophantine equations.	2012	Karim Belabas Frits Beukers Pierrick Gaudry William G. McCallum Bjorn Poonen Samir Siksek Michael Stoll Mark E. Watkins
+ PDF Chat	Another 80-dimensional extremal lattice	2012	Mark E. Watkins
+	Distinguishability of infinite groups and graphs	2011	Simon M. Smith Thomas W. Tucker Mark E. Watkins
+	Passage to Abstract Mathematics	2011	Mark E. Watkins Jeffrey L. Meyer
+ PDF Chat	Computing with Hecke Grössencharacters	2011	Mark E. Watkins
+	Distinguishability of infinite groups and graphs	2011	Simon Smith Thomas W. Tucker Mark E. Watkins
+ PDF Chat	Congruent Number Theta Coefficients to 1012	2010	William B. Hart Gonzalo Tornaría Mark E. Watkins
+ PDF Chat	On the Extremality of an 80-Dimensional Lattice	2010	Damien Stehlé Mark E. Watkins
+	Magma - A Tool for Number Theory	2010	John Cannon Steve Donnelly Claus Fieker Mark E. Watkins
+ PDF Chat	Euler Factors and Local Root Numbers for Symmetric Powers of Elliptic Curves	2009	Neil Dummigan Phil Martin Mark E. Watkins
+ PDF Chat	Critical Values of Symmetric Power L-functions	2009	Neil Dummigan Mark E. Watkins
+	Growth of Edge-Homogeneous Tessellations	2008	Stephen J. Graves Tomaž Pisanski Mark E. Watkins
+ PDF Chat	Some Heuristics about Elliptic Curves	2008	Mark E. Watkins
+ PDF Chat	On elliptic curves and random matrix theory	2008	Mark E. Watkins
+ PDF Chat	Average ranks of elliptic curves: Tension between data and conjecture	2007	Baur Bektemirov Barry Mazur William Stein Mark E. Watkins
+	None	2006	C. Paul Bonnington R. Bruce Richter Mark E. Watkins
+	Between ends and fibers	2006	C. Paul Bonnington R. Bruce Richter Mark E. Watkins
+	Covalence sequences of planar vertex-homogeneous maps	2006	Jana S ̆iagiová Mark E. Watkins
+	A note on integral points on elliptic curves	2006	Mark E. Watkins Noam D. Elkies
+ PDF Chat	A note on integral points on elliptic curves	2006	Mark E. Watkins
+ PDF Chat	Symmetric Powers of Elliptic Curve L-Functions	2006	Phil Martin Mark E. Watkins
+	Some heuristics about elliptic curves	2006	Mark E. Watkins
+	Symmetric powers of elliptic curve L-functions	2006	Phil Martin Mark E. Watkins
+	A note on integral points on elliptic curves	2006	Mark E. Watkins Noam D. Elkies
+	Cayley maps	2005	R. Bruce Richter Jozef Širáň Robert Jajcay Thomas W. Tucker Mark E. Watkins
+	Secondary terms in the number of vanishings of quadratic twists of elliptic curve L-functions	2005	J. Brian Conrey Atul Pocharel Michael Rubinstein Mark E. Watkins
+	Discretisation for odd quadratic twists	2005	J. Brian Conrey Michael Rubinstein N. C. Snaith Mark E. Watkins
+	Some remarks on Heegner point computations	2005	Mark E. Watkins
+	A characterization of infinite planar primitive graphs	2004	Mark E. Watkins Jack E. Graver
+ PDF Chat	Constructing elements in Shafarevich–Tate groups of modular motives	2004	Neil Dummigan William Stein Mark E. Watkins
+	Explicit lower bounds on the modular degree of an elliptic curve	2004	Mark E. Watkins
+	Modular Parametrizations of Neumann-Setzer Elliptic Curves	2004	William Stein Mark E. Watkins
+	Rank distribution in a family of cubic twists	2004	Mark E. Watkins
+ PDF Chat	Elliptic Curves of Large Rank and Small Conductor	2004	Noam D. Elkies Mark E. Watkins
+	Concentric Bilinski diagrams.	2004	Jennifer A. Bruce Mark E. Watkins
+	Elliptic curves of large rank and small conductor	2004	Noam D. Elkies Mark E. Watkins
+	None	2004	William Stein Mark E. Watkins
+ PDF Chat	Class numbers of imaginary quadratic fields	2003	Mark E. Watkins
+ PDF Chat	Real zeros of real odd Dirichlet $L$-functions	2003	Mark E. Watkins
+	A Database of Elliptic Curves — First Report	2002	William Stein Mark E. Watkins
+ PDF Chat	Computing the Modular Degree of an Elliptic Curve	2002	Mark E. Watkins
+	Realizing finite edge‐transitive orientable maps	2001	Jozef Širáň Thomas W. Tucker Mark E. Watkins
+	Geodetic rays and fibers in periodic graphs	2000	Peter Niemeyer Mark E. Watkins
+	Geodetic rays and fibers in periodic graphs	2000	Peter Niemeyer Mark E. Watkins
+	Geodetic Rays and Fibers in One-Ended Planar Graphs	1997	Peter Niemeyer Mark E. Watkins
+	Ends and automorphisms of infinite graphs	1997	Mark E. Watkins
+	On translations of double rays in graphs	1995	Norbert Polat Mark E. Watkins
+	Sur les graphes infinis possedant un groupe d'automorphismes primitif	1994	Mark E. Watkins
+	Vertex-Transitive Graphs That Are Not Cayley Graphs	1990	Mark E. Watkins
+	A note on bounded automorphisms of infinite graphs	1989	Chris Godsil Wilfried Imrich Norbert Seifter Mark E. Watkins Wolfgang Woess
+	The connectivities of locally finite primitive graphs	1989	H. A. Jung Mark E. Watkins
+ PDF Chat	Infinite vertex-transitive, edge-transitive non-$1$-transitive graphs	1989	Carsten Thomassen Mark E. Watkins
+	Infinite Vertex-Transitive, Edge-Transitive Non-1-Transitive Graphs	1989	Carsten Thomassen Mark E. Watkins
+	Counterexamples to two conjectures about distance sequences	1987	Mark E. Watkins James B. Shearer
+	Infinite paths that contain only shortest paths	1986	Mark E. Watkins
+	Fragments and Automorphisms of Infinite Graphs	1984	H. A. Jung Mark E. Watkins
+	On infinite tournaments with regular automorphism groups	1981	Derek Holton Mark E. Watkins
+	Connectivity of infinite graphs having a transitive torsion group action	1980	László Babai Mark E. Watkins
+	On the cayley index of a group	1978	Mark E. Watkins
+	On the connectivities of finite and infinite graphs	1977	H. A. Jung Mark E. Watkins
+	On the structure of infinite vertex-transitive graphs	1977	H. A. Jung Mark E. Watkins
+	Two Famous Problems	1977	Jack E. Graver Mark E. Watkins
+	Matchings and Related Structures	1977	Jack E. Graver Mark E. Watkins
+	Separation and Connectivity in Multigraphs	1977	Jack E. Graver Mark E. Watkins
+	On automorphism groups of Cayley graphs	1976	Wilfried Imrich Mark E. Watkins
+	Graphical regular representations of free products of groups	1976	Mark E. Watkins
+	Graphical regular representations of alternating, symmetric, and miscellaneous small groups	1974	Mark E. Watkins
+	Graphical regular representations of alternating, symmetric, and miscellaneous small groups	1973	Mark E. Watkins
+ PDF Chat	Graphical Regular Representations of Non-Abelian Groups, I	1972	Lewis A. Nowitz Mark E. Watkins
+ PDF Chat	Graphical Regular Representations of Non-Abelian Groups, II	1972	Lewis A. Nowitz Mark E. Watkins
+	On graphical regular representations of direct products of groups	1972	Mark E. Watkins Lewis A. Nowitz
+	On graphical regular representations of Cn × Q	1972	Mark E. Watkins
+	On the action of non-Abelian groups on graphs	1971	Mark E. Watkins
+	The groups of the generalized Petersen graphs	1971	Roberto Frucht Jack E. Graver Mark E. Watkins
+	Connectivity of transitive graphs	1970	Mark E. Watkins
+	On the existence of certain disjoint arcs in graphs	1968	Mark E. Watkins
+	A Lower Bound for the Number of Vertices of a Graph	1967	Mark E. Watkins
+ PDF Chat	Cycles and Connectivity in Graphs	1967	Mark E. Watkins Dale M. Mesner

Common Coauthors

Coauthor	Papers Together
Jack E. Graver	8
Thomas W. Tucker	7
Simon M. Smith	5
Wilfried Imrich	5
William Stein	5
Stephen J. Graves	4
H. A. Jung	4
Noam D. Elkies	4
Jozef Širáň‬	3
Lewis A. Nowitz	3
Neil Dummigan	3
Simon Smith	3
Phil Martin	3
Peter Niemeyer	3
Thomas W. Tucker	2
Michael Rubinstein	2
C. Paul Bonnington	2
J. Brian Conrey	2
R. Bruce Richter	2
Carsten Thomassen	2
Norbert Polat	1
Atul Pocharel	1
Pierrick Gaudry	1
Damien Stehlé	1
Baur Bektemirov	1
Stephen Robert Donnelly	1
Norbert Seifter	1
John Kevin Doyle	1
Nicholas F. Rogers	1
Michael Stoll	1
Steve Donnelly	1
Chris Godsil	1
Karim Belabas	1
Frits Beukers	1
Jana S ̆iagiová	1
Noam D. Elkies	1
Barry Mazur	1
R. Bruce Richter	1
James B. Shearer	1
Tomaž Pisanski	1
László Babai	1
Samir Siksek	1
Andrew Granville	1
Gonzalo Tornaría	1
Tom Fisher	1
Roberto Frucht	1
Jeffrey L. Meyer	1
William G. McCallum	1
Claus Fieker	1
Dale M. Mesner	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+	Automorphisms and endomorphisms of infinite locally finite graphs	1973	R. Halin	18
+ PDF Chat	On a class of fixed-point-free graphs	1958	Gert Sabidussi	14
+	A note on fragments of infinite graphs	1981	H. A. Jung	13
+	The Magma Algebra System I: The User Language	1997	Wieb Bosma John Cannon Catherine Playoust	12
+	Notes on elliptic curves. II.	1965	B. J. Birch H. P. F. Swinnerton-Dyer	12
+	Heegner points and derivatives ofL-series	1986	Benedict H. Gross Don Zagier	11
+	On the structure of infinite vertex-transitive graphs	1977	H. A. Jung Mark E. Watkins	11
+	Modular Elliptic Curves and Fermat's Last Theorem	1995	Andrew Wiles	10
+ PDF Chat	Graphical Regular Representations of Non-Abelian Groups, I	1972	Lewis A. Nowitz Mark E. Watkins	9
+	Algorithms for Modular Elliptic Curves	1992	J. E. Cremona	9
+	On the action of non-Abelian groups on graphs	1971	Mark E. Watkins	9
+	Fragments and Automorphisms of Infinite Graphs	1984	H. A. Jung Mark E. Watkins	9
+ PDF Chat	The behavior of the Mordell-Weil group of elliptic curves	1990	Armand Brumer Francis McGuinness	9
+	On the modularity of elliptic curves over 𝐐: Wild 3-adic exercises	2001	Christophe Breuil Brian Conrad Fred Diamond Richard Taylor	8
+	Infinite paths that contain only shortest paths	1986	Mark E. Watkins	8
+	Connectivity in Graphs	1966	W. T. Tutte	8
+ PDF Chat	Computing the Modular Degree of an Elliptic Curve	2002	Mark E. Watkins	8
+	Edge‐transitive planar graphs	1987	Branko Grünbaum G. C. Shephard	8
+	Iwasawa theory for the symmetric square of an elliptic curve.	1987	Carsten Schmidt John D. Coates	7
+	Decomposing Ends of Locally Finite Graphs	1995	Heinz Jung Peter Niemeyer	7
+	On the frequency of vanishing of quadratic twists of modular L-functions	2000	JB Conrey JP Keating MO Rubinstein N C Snaith	7
+	A Database of Elliptic Curves — First Report	2002	William Stein Mark E. Watkins	7
+	On the non-existence of graphs with transitive generalized dicyclic groups	1968	Lewis A. Nowitz	7
+ PDF Chat	Cycles, L-functions and triple products of elliptic curves.	1997	Joe Buhler Chad Schoen Jakob Top	6
+	Stickelberger elements and modular parametrizations of elliptic curves	1989	Glenn Stevens	6
+	Geodetic Rays and Fibers in One-Ended Planar Graphs	1997	Peter Niemeyer Mark E. Watkins	6
+ PDF Chat	Graphical Regular Representations of Non-Abelian Groups, II	1972	Lewis A. Nowitz Mark E. Watkins	6
+	Hecke operators on ?0(m)	1970	A. O. L. Atkin Joseph Lehner	6
+	On translations of double rays in graphs	1995	Norbert Polat Mark E. Watkins	6
+	A note on bounded automorphisms of infinite graphs	1989	Chris Godsil Wilfried Imrich Norbert Seifter Mark E. Watkins Wolfgang Woess	6
+	Graphical regular representations of free products of groups	1976	Mark E. Watkins	6
+	A note on the growth of transitive graphs	1988	Wilfried Imrich Norbert Seifter	6
+	Graphical regular representations of alternating, symmetric, and miscellaneous small groups	1974	Mark E. Watkins	5
+	A Course in Computational Algebraic Number Theory	1993	Henri Cohen	5
+	Ring-Theoretic Properties of Certain Hecke Algebras	1995	Richard Taylor Andrew Wiles	5
+	Elliptic Curves of Prime Conductor	1975	Bennett Setzer	5
+	On the connectivities of finite and infinite graphs	1977	H. A. Jung Mark E. Watkins	5
+	Regular line-symmetric graphs	1967	Jon Folkman	5
+	Tilings and Patterns.	1988	Solomon W. Golomb Branko Grünbaum G. C. Shephard	5
+	On the Holomorphy of Certain Dirichlet Series	1975	Goro Shimura	5
+	The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer	1976	Dorian Goldfeld	5
+ PDF Chat	On a theorem of Sabidussi	1964	Chong-Yun Chao	5
+	Advanced Topics in Computational Number Theory	2011	Henri Cohen	4
+	Cuspidality of symmetric powers with applications	2002	Henry H. Kim Freydoon Shahidi	4
+	On graphical regular representations of Cn × Q	1972	Mark E. Watkins	4
+ PDF Chat	Modularity of certain potentially Barsotti-Tate Galois representations	1999	Brian Conrad Fred Diamond Richard Taylor	4
+ PDF Chat	A complete determination of the complex quadratic fields of class-number one.	1967	H. Stärk	4
+	Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂	2002	Henry Kim	4
+	Connectivity of transitive graphs	1970	Mark E. Watkins	4
+	Good Reduction of Abelian Varieties	1968	Jean-Pierre Serre John Tate	4