Pete L. Clark

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All published works

Action	Title	Year	Authors
+	Ax's Lemma and Ax's Theorem in the Aichinger-Moosbauer calculus	2024	Pete L. Clark Nicholas Triantafillou
+ PDF Chat	Densities of integer sets represented by quadratic forms	2023	Pete L. Clark Paul Pollack Jeremy Rouse Katherine Thompson
+	Densities of integer sets represented by quadratic forms	2023	Pete L. Clark Paul Pollack Jeremy Rouse Katherine Thompson
+	Functional degrees and arithmetic applications II: The Group-Theoretic Prime Ax-Katz Theorem	2023	Pete L. Clark Uwe Schauz
+	Functional degrees and arithmetic applications III: Beyond Prime Exponent	2023	Pete L. Clark Uwe Schauz
+ PDF Chat	Functional degrees and arithmetic applications I: The set of functional degrees	2022	Pete L. Clark Uwe Schauz
+	The least degree of a CM point on a modular curve	2022	Pete L. Clark Tyler Genao Paul Pollack Frederick Saia
+	Restricted Variable Chevalley-Warning Theorems	2022	Anurag Bishnoi Pete L. Clark
+	CM Elliptic Curves: Volcanoes, Reality and Applications, Part II	2022	Pete L. Clark Frederick Saia
+	CM Elliptic Curves: Volcanoes, Reality and Applications	2022	Pete L. Clark
+ PDF Chat	Chevalley–Warning at the boundary	2021	Pete L. Clark Tyler Genao Frederick Saia
+	Acyclotomy of torsion in the CM case	2020	Michael Chou Pete L. Clark Marko Milošević
+ PDF Chat	Torsion points and isogenies on CM elliptic curves	2020	Abbey Bourdon Pete L. Clark
+ PDF Chat	Torsion points and Galois representations on CM elliptic curves	2020	Abbey Bourdon Pete L. Clark
+	Reciprocity by resultant in $k[t]$	2020	Pete L. Clark Paul Pollack
+	A generalization of the theorems of Chevalley-Warning and Ax-Katz via polynomial substitutions	2019	Ioulia N. Baoulina Anurag Bishnoi Pete L. Clark
+	Rabinowitsch times six	2019	Pete L. Clark
+ PDF Chat	The Instructor’s Guide to Real Induction	2019	Pete L. Clark
+ PDF Chat	Warning’s second theorem with relaxed outputs	2018	Pete L. Clark
+ PDF Chat	ABC and the Hasse principle for quadratic twists of hyperelliptic curves	2018	Pete L. Clark Lori D. Watson
+ PDF Chat	Pursuing polynomial bounds on torsion	2018	Pete L. Clark Paul Pollack
+	Typically bounding torsion	2018	Pete L. Clark Marko Milošević Paul Pollack
+	A note on Golomb topologies	2018	Pete L. Clark Noah Lebowitz-Lockard Paul Pollack
+ PDF Chat	On Zeros of a Polynomial in a Finite Grid	2018	Anurag Bishnoi Pete L. Clark Aditya Potukuchi John R. Schmitt
+	Hasse principle violations for Atkin-Lehner twists of Shimura curves	2017	Pete L. Clark James Stankewicz
+	A Note on rings of finite rank	2017	Pete L. Clark
+	A generalization of the Chevalley-Warning theorem	2017	Ioulia N. Baoulina Anurag Bishnoi Pete L. Clark
+ PDF Chat	Algebraic curves uniformized by congruence subgroups of triangle groups	2017	Pete L. Clark John Voight
+	Typically bounding torsion	2017	Pete L. Clark Marko Milošević Paul Pollack
+	Pursuing polynomial bounds on torsion	2017	Pete L. Clark Paul Pollack
+	The number of atoms in a primefree atomic domain	2017	Pete L. Clark Saurabh Gosavi Paul Pollack
+	The cardinal Krull dimension of a ring of holomorphic functions	2017	Pete L. Clark
+ PDF Chat	The truth about torsion in the CM case, II	2017	Pete L. Clark Paul Pollack
+	A simultaneous generalization of the theorems of Chevalley-Warning and Morlaye	2017	Pete L. Clark
+	Typically bounding torsion	2017	Pete L. Clark Marko Milosevic Paul Pollack
+	Pursuing polynomial bounds on torsion	2017	Pete L. Clark Paul Pollack
+	Hasse Principle Violations for Atkin-Lehner Twists of Shimura Curves	2016	Pete L. Clark James Stankewicz
+ PDF Chat	There are genus one curves of every index over every infinite, finitely generated field	2016	Pete L. Clark Allan Lacy
+	Anatomy of torsion in the CM case	2016	Abbey Bourdon Pete L. Clark Paul Pollack
+	A note on rings of finite rank	2016	Pete L. Clark
+	The Euclidean criterion for irreducibles	2016	Pete L. Clark
+	Torsion points on CM elliptic curves over real number fields	2016	Abbey Bourdon Pete L. Clark James Stankewicz
+	The Euclidean criterion for irreducibles	2016	Pete L. Clark
+	The truth about torsion in the CM case, II	2016	Pete L. Clark Paul Pollack
+	Hasse Principle Violations for Atkin-Lehner Twists of Shimura Curves	2016	Pete L. Clark James Stankewicz
+	A note on rings of finite rank	2016	Pete L. Clark
+	On Zeros of a Polynomial in a Finite Grid	2015	Anurag Bishnoi Pete L. Clark Aditya Potukuchi John R. Schmitt
+	The truth about torsion in the CM case	2015	Pete L. Clark Paul Pollack
+	Algebraic curves uniformized by congruence subgroups of triangle groups	2015	Pete L. Clark John Voight
+	The truth about torsion in the CM case	2015	Pete L. Clark Paul Pollack
+	The number of atoms in an atomic domain	2015	Pete L. Clark Saurabh Gosavi Paul Pollack
+	Anatomy of torsion in the CM case	2015	Abbey Bourdon Pete L. Clark Paul Pollack
+	On zeros of a polynomial in a finite grid	2015	Anurag Bishnoi Pete L. Clark Aditya Potukuchi John R. Schmitt
+	Algebraic curves uniformized by congruence subgroups of triangle groups	2015	Pete L. Clark John Voight
+	The truth about torsion in the CM case	2015	Pete L. Clark Paul Pollack
+	Fattening up Warning's Second Theorem	2015	Pete L. Clark
+	Torsion Points on CM Elliptic Curves Over Real Number Fields	2014	Abbey Bourdon Pete L. Clark James Stankewicz
+	Extending the Zolotarev–Frobenius approach to quadratic reciprocity	2014	Adrian Brunyate Pete L. Clark
+ PDF Chat	The Combinatorial Nullstellensätze Revisited	2014	Pete L. Clark
+	The Combinatorial Nullstellensätze Revisited	2014	Pete L. Clark
+	The Combinatorial Nullstellens\"atze Revisited	2014	Pete L. Clark
+ PDF Chat	GONI: PRIMES REPRESENTED BY BINARY QUADRATIC FORMS	2014	Pete L. Clark Jacob Hicks Hans Parshall Katherine Thompson
+	Abstract Geometry of Numbers: Linear Forms	2014	Pete L. Clark
+	There are genus one curves of every index over every infinite, finitely generated field	2014	Pete L. Clark Allan Lacy
+ PDF Chat	A Note on Euclidean Order Types	2014	Pete L. Clark
+ PDF Chat	Euclidean quadratic forms and ADC forms II: integral forms	2014	Pete L. Clark William C. Jagy
+	Absolute Convergence in Ordered Fields	2014	Pete L. Clark Niels J. Diepeveen
+	Warning's Second Theorem with Resricted Variables	2014	Pete L. Clark Aden Forrow John R. Schmitt
+ PDF Chat	Computation on elliptic curves with complex multiplication	2014	Pete L. Clark Patrick Corn Alex Rice James Stankewicz
+	Torsion Points on CM Elliptic Curves Over Real Number Fields	2014	Abbey Bourdon Pete L. Clark James Stankewicz
+	The Combinatorial Nullstellensätze Revisited	2014	Pete L. Clark
+	Abstract Geometry of Numbers: Linear Forms	2014	Pete L. Clark
+	There are genus one curves of every index over every infinite, finitely generated field	2014	Pete L. Clark Allan Lacy
+	GoNI: Primes Represented by Binary Quadratic Forms.	2013	Pete L. Clark Jacob Hicks Hans Parshall Katherine Thompson
+ PDF Chat	Graph Derangements	2013	Pete L. Clark
+	Graph Derangements	2013	Pete L. Clark
+	TORSION POINTS ON ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION (WITH AN APPENDIX BY ALEX RICE)	2012	Pete L. Clark Brian Cook James Stankewicz Jim H Stankewicz
+	Euclidean Quadratic Forms and ADC Forms I	2012	Pete L. Clark
+	A Note on Euclidean Order Types	2012	Pete L. Clark
+	The Instructor's Guide to Real Induction	2012	Pete L. Clark
+	Covering Numbers in Linear Algebra	2012	Pete L. Clark
+ PDF Chat	Euclidean quadratic forms and ADC forms: I	2012	Pete L. Clark
+	GoNII: Universal Quaternary Quadratic Forms.	2012	Pete L. Clark Jacob Hicks Katherine Thompson Nathan Walters
+	Euclidean Quadratic Forms and ADC Forms I	2012	Pete L. Clark
+	The Instructor's Guide to Real Induction	2012	Pete L. Clark
+	A Note on Euclidean Order Types	2012	Pete L. Clark
+	Covering Numbers in Linear Algebra	2011	Pete L. Clark
+	ON THE INDICES OF CURVES OVER LOCAL FIELDS (2011 VERSION)	2011	Pete L. Clark
+ PDF Chat	Period, index and potential, III	2010	Pete L. Clark Shahed Sharif
+	THUE'S LEMMA AND IDONEAL QUADRATIC FORMS	2010	Pete L. Clark
+	2010 SUMMER COURSE ON MODEL THEORY: CHAPTER 1	2010	Pete L. Clark
+	INTEGERS REPRESENTED BY IDONEAL QUADRATIC FORMS	2010	Pete L. Clark
+	2010 SUMMER COURSE ON MODEL THEORY	2010	Pete L. Clark
+	SUMMER 2010 COURSE ON MODEL THEORY AND ITS APPLICATIONS	2010	Pete L. Clark
+ PDF Chat	The period-index problem in WC-groups IV: a local transition theorem	2010	Pete L. Clark
+ PDF Chat	Elliptic Dedekind Domains Revisited	2009	Pete L. Clark
+ PDF Chat	On the Hasse principle for Shimura curves	2009	Pete L. Clark
+	Torsion points on elliptic curves with complex multiplication	2009	Pete L. Clark Brian Cook James Stankewicz
+	Curves over global fields violating the Hasse Principle	2009	Pete L. Clark
+	Period-index problems in WC-groups IV: a local transition theorem	2009	Pete L. Clark
+ PDF Chat	AN "ANTI-HASSE PRINCIPLE" FOR PRIME TWISTS	2008	Pete L. Clark
+ PDF Chat	Local Bounds for Torsion Points on Abelian Varieties	2008	Pete L. Clark Xavier Xarles
+	Elliptic Dedekind Domains Revisited	2008	Pete L. Clark
+	Algebra & Number Theory	2008	Pete L. Clark Shahed Sharif
+	Period, index and potential sha	2008	Pete L. Clark Shahed Sharif
+	Local Bounds for Torsion Points on Abelian Varieties	2008	Pete L. Clark Xavier Xarles
+ PDF Chat	On the indices of curves over local fields	2007	Pete L. Clark
+ PDF Chat	Abelian points on algebraic varieties	2007	Pete L. Clark
+ PDF Chat	Galois groups via Atkin-Lehner twists	2006	Pete L. Clark
+	Abelian points on algebraic curves	2006	Pete L. Clark
+ PDF Chat	On elementary equivalence, isomorphism and isogeny	2006	Pete L. Clark
+ PDF Chat	There are genus one curves of every index over every number field	2006	Pete L. Clark
+	On the indices of curves over local fields	2006	Pete L. Clark
+	An "Anti-Hasse Principle" for Prime Twists	2006	Pete L. Clark
+	On the Number of Representations of an Integer by a Linear Form	2005	Gil Alon Pete L. Clark Burnside Hall Sherbrooke West
+	On Serre's Complement to Shih's Theorem	2005	Pete L. Clark
+	The period–index problem in WC-groups I: elliptic curves	2005	Pete L. Clark
+	On the Hasse principle for Shimura curves	2005	Pete L. Clark
+	Galois Groups Via Atkin-Lehner Twists	2005	Pete L. Clark
+	Bounds for torsion on abelian varieties with integral moduli	2004	Pete L. Clark
+	On elementary equivalence, isomorphism and isogeny of arithmetic function fields	2004	Pete L. Clark
+	The period-index problem in WC-groups II: abelian varieties	2004	Pete L. Clark
+	There are genus one curves of every index over every number field	2004	Pete L. Clark
+	The period-index problem in WC-groups I: elliptic curves	2004	Pete L. Clark
+	Rational Points on Atkin-Lehner Quotients of Shimura Curves	2003	Pete L. Clark

Common Coauthors

Coauthor	Papers Together
Paul Pollack	14
James Stankewicz	9
Abbey Bourdon	7
Paul Pollack	6
Anurag Bishnoi	6
John R. Schmitt	4
Jacob Hicks	3
Marko Milošević	3
Uwe Schauz	3
John Voight	3
Frederick Saia	3
Shahed Sharif	3
Aditya Potukuchi	3
Katherine Thompson	3
Allan Lacy	3
Brian Cook	2
Saurabh Gosavi	2
Katherine Thompson	2
Hans Parshall	2
Jeremy Rouse	2
Tyler Genao	2
Ioulia N. Baoulina	2
Xavier Xarles	2
Lori D. Watson	1
Gil Alon	1
Noah Lebowitz-Lockard	1
Michael Chou	1
Adrian Brunyate	1
Burnside Hall	1
Nicholas Triantafillou	1
Aden Forrow	1
Patrick Corn	1
William C. Jagy	1
Sherbrooke West	1
Nathan Walters	1
Alex Rice	1
Niels J. Diepeveen	1
Marko Milosevic	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	The Arithmetic of Elliptic Curves	1986	Joseph H. Silverman	18
+	Bornes pour la torsion des courbes elliptiques sur les corps de nombres	1996	Lo x EF c Merel	17
+	Torsion points on abelian varieties of CM-type	1988	Alice Silverberg	15
+	Advanced Topics in the Arithmetic of Elliptic Curves	1994	Joseph H. Silverman	14
+	Sur le nombre de points de torsion rationnels sur une courbe elliptique	1999	Marc Hindry Joseph H. Silverman	13
+	Principal Homogeneous Spaces Over Abelian Varieties	1958	Serge Lang John Tate	13
+	TORSION POINTS ON ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION (WITH AN APPENDIX BY ALEX RICE)	2012	Pete L. Clark Brian Cook James Stankewicz Jim H Stankewicz	12
+	Bounding the torsion in CM elliptic curves	1998	Dipendra Prasad C. S. Yogananda	12
+	An Introduction to the Theory of Numbers. By G. H. Hardy and E. M. Wright. 2nd edition. Pp. xvi, 407 25s. 1945. (Oxford)	1946	T. A. A. B.	11
+	The truth about torsion in the CM case	2015	Pete L. Clark Paul Pollack	11
+ PDF Chat	Primes of the form x2 + ny2: Fermat, class field theory, and complex multiplication	1990	David A. Cox	11
+ PDF Chat	Points of finite order on elliptic curves with complex multiplication	1974	Loren D. Olson	10
+	Points of finite order on abelian varieties	1980	Fedor Bogomolov	10
+	The Period-Index Problem for Elliptic Curves	1968	Stephen Lichtenbaum	10
+ PDF Chat	Torsion bounds for elliptic curves and Drinfeld modules	2010	Florian Breuer	9
+	The Period-Index Obstruction for Elliptic Curves	2002	Catherine O’Neil	8
+	Rational torsion in complex-multiplication elliptic curves	1989	James L. Parish	8
+ PDF Chat	On the Hasse principle for Shimura curves	2009	Pete L. Clark	8
+ PDF Chat	Algebraically Solvable Problems: Describing Polynomials as Equivalent to Explicit Solutions	2008	Uwe Schauz	7
+	Propri�t�s galoisiennes des points d'ordre fini des courbes elliptiques	1971	Jean-Pierre Serre	7
+ PDF Chat	Abelian varieties over finite fields	1969	William C. Waterhouse	7
+ PDF Chat	There are genus one curves of every index over every number field	2006	Pete L. Clark	7
+	None	1996	Dan Abramovich	7
+ PDF Chat	The Cassels-Tate Pairing on Polarized Abelian Varieties	1999	Bjorn Poonen Michael Stoll	7
+ PDF Chat	Computation on elliptic curves with complex multiplication	2014	Pete L. Clark Patrick Corn Alex Rice James Stankewicz	6
+ PDF Chat	Local Bounds for Torsion Points on Abelian Varieties	2008	Pete L. Clark Xavier Xarles	6
+	Torsion points on CM elliptic curves over real number fields	2016	Abbey Bourdon Pete L. Clark James Stankewicz	6
+	Zeroes of Polynomials Over Finite Fields	1964	James Ax	6
+	Advanced Topics in Computational Number Theory	2011	Henri Cohen	6
+	$WC$-groups over $p$-adic fields	1958	John Tate	6
+ PDF Chat	Primes of the form x<sup>2 </sup>+ ny<sup>2</sup>	2012	K. Raja Rama Gandhi	6
+ PDF Chat	An Introduction To The Theory Of Numbers	2008	G. H. Hardy E. M. Wright	6
+ PDF Chat	Quadratic forms that represent almost the same primes	2007	John Voight	5
+ PDF Chat	Solvable Points on Projective Algebraic Curves	2004	Ambrus Pál	5
+	ON THE MORDELL-WEIL AND SHAFAREVICH-TATE GROUPS FOR WEIL ELLIPTIC CURVES	1989	V. A. Kolyvagin	5
+	Good Reduction of Abelian Varieties	1968	Jean-Pierre Serre John Tate	5
+	Periode und Index Eines Prinzipal-Homogenen Raumes �ber Gewissen Abelschen Variet�ten	1973	Lothar Gerritzen	5
+	Anatomy of torsion in the CM case	2016	Abbey Bourdon Pete L. Clark Paul Pollack	5
+ PDF Chat	Ranks of twists of elliptic curves and Hilbert’s tenth problem	2010	Barry Mazur Karl Rubin	5
+	Real Points on Shimura Curves	1983	A. P. Ogg	5
+	Rational Points on Atkin-Lehner Quotients of Shimura Curves	2003	Pete L. Clark	5
+ PDF Chat	Universal Bounds on the Torsion of Elliptic Curves	1976	Daniel S. Kubert	5
+ PDF Chat	Hyperelliptic modular curves	1974	A. P. Ogg	5
+	Introduction to Quadratic Forms over Fields	2004	T. Y. Lam	5
+	Cohen-Kaplansky domains: Integral domains with a finite number of irreducible elements	1992	D. D. Anderson J. L. Mott	5
+	Local diophantine properties of Shimura curves	1985	Bruce W. Jordan Ron Livné	5
+	Introduction to Quadratic Forms	1973	O. T. O’Meara	5
+	Multiplicative Theory of Ideals.	1973	H. H. Brungs Max D. Larsen Paul McCarthy	5
+ PDF Chat	On the structure of principal ideal rings	1968	Thomas W. Hungerford	5
+	Integral models of certain Shimura curves	1997	Kevin Buzzard	5