Team > Prof. Dr. Michael Stoll

2023

Kiermaier, Michael; Kurz, Sascha; Solé, Patrick; Stoll, Michael; Wassermann, Alfred
On strongly walk regular graphs, triple sum sets and their codes
in Designs, Codes and Cryptography volume 91 (2023) . - page 645-675
doi:10.1007/s10623-022-01118-z ...

Derickx, Maarten; Kamienny, Sheldon; Stein, William; Stoll, Michael
Torsion points on elliptic curves over number fields of small degree
in Algebra & Number Theory volume 17 (2023) issue 2. - page 267-308
doi:10.2140/ant.2023.17.267 ...

2022

Fu, Hang; Stoll, Michael
Elliptic curves with common torsion x-coordinates and hyperelliptic torsion packets
in Proceedings of the American Mathematical Society volume 150 (2022) . - page 5137-5149
doi:10.1090/proc/16102 ...
rev.: MathSciNet

Keller, Timo; Stoll, Michael
Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces
in Comptes Rendus Mathématique volume 360 (2022) . - page 483-489
doi:10.5802/crmath.313 ...
rev.: MathSciNet

Reinke, Bernhard; Schleicher, Dierk; Stoll, Michael
The Weierstrass–Durand–Kerner root finder is not generally convergent
in Mathematics of Computation volume 92 (2022) issue 340. - page 839-866
doi:10.1090/mcom/3783 ...
rev.: MathSciNet

2021

Bruin, Peter; Derickx, Maarten; Stoll, Michael
Elliptic curves with a point of order 13 defined over cyclic cubic fields
in Functiones et Approximatio Commentarii Mathematici volume 65 (2021) issue 2. - page 191-197
doi:10.7169/facm/1945 ...
rev.: MathSciNet

2020

DeMark, David; Hindes, Wade; Jones, Rafe; Misplon, Moses; Stoll, Michael; Stoneman, Michael
Eventually stable quadratic polynomials over ℚ
in New York Journal of Mathematics volume 26 (2020) . - page 526-561
http://nyjm.albany.edu/j/2020/26-25.html

Freitas, Nuno; Naskręcki, Bartosz; Stoll, Michael
The generalized Fermat equation with exponents 2, 3, n
in Compositio Mathematica volume 156 (2020) issue 1. - page 77-113
doi:10.1112/s0010437x19007693 ...

Sawin, Will; Shusterman, Mark; Stoll, Michael
Irreducibility of polynomials with a large gap
in Acta Arithmetica volume 192 (2020) issue 2. - page 111-139
doi:10.4064/aa180526-12-6 ...

2019

Stoll, Michael
Diagonal genus 5 curves, elliptic curves over ℚ(t), and rational diophantine quintuples
in Acta Arithmetica volume 190 (2019) issue 3. - page 239-261
doi:10.4064/aa180416-4-10 ...

Vishkautsan, Solomon; Stoll, Michael
Quadratic rational functions with a rational periodic critical point of period 3 : with 5 p App ...
in Journal de Théorie des Nombres de Bordeaux volume 31 (2019) issue 1. - page 49-79
doi:10.5802/jtnb.1068 ...

Hutz, Benjamin; Stoll, Michael
Smallest representatives of SL(2,ℤ)-orbits of binary forms and endomorphisms of ℙ¹
in Acta Arithmetica volume 189 (2019) issue 3. - page 283-308
doi:10.4064/aa180618-9-12 ...

Stoll, Michael
Uniform bounds for the number of rational points on hyperelliptic curves of small Mordell-Weil ...
in Journal of the European Mathematical Society volume 21 (2019) issue 3. - page 923-956
doi:10.4171/JEMS/857 ...

Checcoli, Sara; Veneziano, Francesco; Viada, Evelina; Stoll, Michael
The explicit Mordell conjecture for families of curves
in Forum of Mathematics, Sigma volume 7 (2019)
doi:10.1017/fms.2019.20 ...

2018

Kurz, Sascha; Stoll, Michael; Worthmann, Karl
Angewandte Mathematik : ein Lehrbuch für Lehramtsstudierende
Berlin : Springer, 2018. - XVIII + 210 page
doi:10.1007/978-3-662-56705-0 ...

2017

Stoll, Michael
Chabauty without the Mordell-Weil group
Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory
Cham : Springer, 2017. - page 623-663
doi:10.1007/978-3-319-70566-8_28 ...

Stoll, Michael
An explicit theory of heights for hyperelliptic Jacobians of genus three
Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory
Cham : Springer, 2017. - page 665-715
doi:10.1007/978-3-319-70566-8_29 ...

Bauer, Ingrid; Stoll, Michael
Geometry and arithmetic of primary Burniat surfaces
in Mathematische Nachrichten volume 290 (2017) issue 14–15. - page 2132-2153
doi:10.1002/mana.201600282 ...
rev.: AMS MatSciNet

Stoll, Michael
Simultaneous torsion in the Legendre family
in Experimental Mathematics volume 26 (2017) issue 4. - page 446-459
doi:10.1080/10586458.2016.1201443 ...

2016

Müller, Jan Steffen; Stoll, Michael
Canonical heights on genus-2 Jacobians
in Algebra & Number Theory volume 10 (2016) issue 10. - page 2153-2234
doi:10.2140/ant.2016.10.2153 ...

Müller, Jan Steffen; Stoll, Michael
Computing canonical heights on elliptic curves in quasi-linear time
in LMS Journal of Computation and Mathematics volume 19 (2016) . - page 391-405
doi:10.1112/S1461157016000139 ...

Bruin, Nils; Poonen, Bjorn; Stoll, Michael
Generalized explicit descent and its application to curves of genus 3
in Forum of Mathematics, Sigma volume 4 (2016)
doi:10.1017/fms.2016.1 ...

2015

Stoll, Michael
Descent and covering collections
Advances on superelliptic curves and their applications : Including papers based on the NATO Advanced Study Institute (ASI) on Hyperelliptic Curve Cryptography held in Ohrid, August 25-September 5, 2014
Amsterdam : IOS Press, 2015. - page 176-193 . - (NATO Science for Peace and Security : Series D, Information and Communication Security; 41)
doi:10.3233/978-1-61499-520-3-176 ...

Cremona, John E.; Fisher, Tom A.; O'Neil, C.; Simon, D.; Stoll, Michael
Explicit n-descent on elliptic curves III. Algorithms
in Mathematics of Computation volume 84 (2015) issue 292. - page 895-922
doi:10.1090/S0025-5718-2014-02858-5 ...

2014

Siksek, Samir; Stoll, Michael
The generalised Fermat equation x²+y³=z¹⁵
in Archiv der Mathematik volume 102 (2014) . - page 411-421
doi:10.1007/s00013-014-0639-z ...

Poonen, Bjorn; Stoll, Michael
Most odd degree hyperelliptic curves have only one rational point
in Annals of Mathematics volume 180 (2014) issue 3. - page 1137-1166
doi:10.4007/annals.2014.180.3.7 ...

Greenberg, Ralph; Rubin, Karl; Silverberg, Alice; Stoll, Michael
On elliptic curves with an isogeny of degree 7
in American Journal of Mathematics volume 136 (2014) issue 1. - page 77-109
doi:10.1353/ajm.2014.0005 ...

Stoll, Michael
Rational points on hyperelliptic curves : recent developments
in Computeralgebra-Rundbrief volume 54 (2014) . - page 10-13
http://www.fachgruppe-computeralgebra.de/data/CA-R ...

2013

Miller, Robert L.; Stoll, Michael
Explicit isogeny descent on elliptic curves
in Mathematics of Computation volume 82 (2013) . - page 513-529
doi:10.1090/S0025-5718-2012-02619-6 ...

Stoll, Michael; van Luijk, Ronald
Explicit Selmer groups for cyclic covers of P¹
in Acta Arithmetica volume 159 (2013) . - page 133-148
doi:10.4064/aa159-2-4 ...

2012

Stoll, Michael
Descent on elliptic curves
Explicit methods in number theory : Rational points & Diophantine equations. Lectures from the Special Trimester held at the Institut Henri Poincaré, Paris, September–December 2004
Paris : Société Mathématique de France, 2012. - page 51-80 . - (Panoramas et Synthèses; 36)

Siksek, Samir; Stoll, Michael
Partial descent on hyperelliptic curves and the generalized Fermat equation x³+y⁴+z⁵=0
in The Bulletin of the London Mathematical Society volume 44 (2012) issue 1. - page 151-166
doi:10.1112/blms/bdr086 ...

Geigant, Edith; Stoll, Michael
Stability of peak solutions of a non-linear transport equation on the circle
in Electronic Journal of Differential Equations volume 2012 (2012) issue 157. - page 1-41
http://www.emis.de/journals/EJDE/Volumes/2012/157/ ...

2011

Stoll, Michael
How to Solve a Diophantine Equation
Schleicher, Dierk ; Lackmann, Malte (Hrsg.): An Invitation to Mathematics : From Competitions to Research
Heidelberg ; Dordrecht ; London ; New York : Springer, 2011. - page 9-19
doi:10.1007/978-3-642-19533-4_2 ...

Faber, Xander; Hutz, Benjamin; Stoll, Michael
On the number of rational iterated preimages of the origin under quadratic dynamical systems
in International Journal of Number Theory volume 7 (2011) issue 7. - page 1781-1806
doi:10.1142/S1793042111004162 ...

Stoll, Michael
Rational points on curves
in Journal de Théorie des Nombres de Bordeaux volume 23 (2011) issue 1. - page 257-277
doi:10.5802/jtnb.760 ...

Stoll, Michael
Reduction theory of point clusters in projective space
in Groups, Geometry, and Dynamics volume 5 (2011) issue 2. - page 553-565
doi:10.4171/GGD/139 ...

2010

Cremona, John E.; Fisher, Tom A.; Stoll, Michael
Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves
in Algebra & Number Theory volume 4 (2010) issue 6. - page 763-820
doi:10.2140/ant.2010.4.763 ...

Bruin, Nils; Stoll, Michael
The Mordell-Weil sieve : proving non-existence of rational points on curves
in LMS Journal of Computation and Mathematics volume 13 (2010) . - page 272-306
doi:10.1112/S1461157009000187 ...

Siksek, Samir; Stoll, Michael
On a problem of Hajdu and Tengely
Hanrot, Guillaume ; Morain, Francois ; Thomé, Emmanuel (Hrsg.): Algorithmic Number Theory : 9th international symposium, ANTS-IX, Nancy, France, July 19-23, 2010, proceedings
Heidelberg : Springer, 2010. - page 316-330 . - (Lecture Notes in Computer Science; 6197)
doi:10.1007/978-3-642-14518-6_25 ...

Fisher, Tom A.; Schaefer, Edward F.; Stoll, Michael
The yoga of the Cassels-Tate pairing
in LMS Journal of Computation and Mathematics volume 13 (2010) . - page 451-460
doi:10.1112/S1461157010000185 ...

2009

Stoll, Michael
Rational Points on Curves of Genus 2 : Experiments and Speculations
Johannes A. Buchmann, John Cremona and Michael E. Pohst (editors): Algorithms and Number Theory
Wadern , 2009 (Dagstuhl Seminar Proceedings; 09221)
http://drops.dagstuhl.de/opus/volltexte/2009/2124/

Cremona, John E.; Fisher, Tom A.; O'Neil, C.; Simon, D.; Stoll, Michael
Explicit n-descent on elliptic curves, II. Geometry
in Journal für die Reine und Angewandte Mathematik (2009) issue 632. - page 63-84
doi:10.1515/CRELLE.2009.050 ...

Stoll, Michael; Walsh, P. G.; Yuan, Pingzhi
On the Diophantine equation X² - (2²ᵐ + 1) Y⁴ = -2²ᵐ
in Acta Arithmetica volume 139 (2009) issue 1. - page 57-63
doi:10.4064/aa139-1-5 ...

Bruin, Nils; Stoll, Michael
Two-cover descent on hyperelliptic curves
in Mathematics of Computation volume 78 (2009) issue 268. - page 2347-2370
doi:10.1090/S0025-5718-09-02255-8 ...

2008

Bruin, Nils; Stoll, Michael
Deciding existence of rational points on curves : an experiment
in Experimental Mathematics volume 17 (2008) issue 2. - page 181-189
http://projecteuclid.org/euclid.em/1227118970

Cremona, John E.; Fisher, Tom A.; O'Neil, C.; Simon, D.; Stoll, Michael
Explicit n-descent on elliptic curves, I. Algebra
in Journal für die Reine und Angewandte Mathematik (2008) issue 615. - page 121-155
doi:10.1515/CRELLE.2008.012 ...

Stoll, Michael
How to obtain global information from computations over finite fields
Dmitry Kaledin, Yuri Tschinkel (editors): Higher-dimensional geometry over finite fields
Amsterdam : IOS Press, 2008. - page 189-196 . - (NATO Science for Peace and Security : Series D, Information and Communication Security; 16)

Bugeaud, Yann; Mignotte, Maurice; Siksek, Samir; Stoll, Michael; Tengely, Szabolcs
Integral points on hyperelliptic curves
in Algebra & Number Theory volume 2 (2008) issue 8. - page 859-885
doi:10.2140/ant.2008.2.859 ...

Stoll, Michael
Rational 6-cycles under iteration of quadratic polynomials
in LMS Journal of Computation and Mathematics volume 11 (2008) . - page 367-380
doi:10.1112/S1461157000000644 ...

2007

Stoll, Michael
Applications of the Mordell-Weil sieve
in Oberwolfach Reports volume 4 (2007) issue 3. - page 1967-1970
doi:10.4171/OWR/2007/34 ...

Stoll, Michael
Finite descent obstructions and rational points on curves
in Algebra & Number Theory volume 1 (2007) issue 4. - page 349-391
doi:10.2140/ant.2007.1.349 ...

Poonen, Bjorn; Schaefer, Edward F.; Stoll, Michael
Twists of X(7) and primitive solutions to x²+y³=z⁷
in Duke Mathematical Journal volume 137 (2007) issue 1. - page 103-158
doi:10.1215/S0012-7094-07-13714-1 ...

2006

Stoll, Michael
Independence of rational points on twists of a given curve
in Compositio Mathematica volume 142 (2006) issue 5. - page 1201-1214
doi:10.1112/S0010437X06002168 ...

Schleicher, Dierk; Stoll, Michael
An introduction to Conway’s games and numbers
in Moscow Mathematical Journal volume 6 (2006) issue 2. - page 359-388
http://www.ams.org/distribution/mmj/vol6-2-2006/sc ...

Stoll, Michael
On the number of rational squares at fixed distance from a fifth power
in Acta Arithmetica volume 125 (2006) issue 1. - page 79-88
doi:10.4064/aa125-1-7 ...

2005

Stoll, Michael
Finite coverings and rational points
in Oberwolfach Reports volume 2 (2005) issue 3. - page 1824-1827
doi:10.4171/OWR/2005/32 ...

2004

Schaefer, Edward F.; Stoll, Michael
How to do a p-descent on an elliptic curve
in Transactions of the American Mathematical Society volume 356 (2004) issue 3. - page 1209-1231
doi:10.1090/S0002-9947-03-03366-X ...

2003

Geigant, Edith; Stoll, Michael
Bifurcation analysis of an orientational aggregation model
in Journal of Mathematical Biology volume 46 (2003) issue 6. - page 537-563
doi:10.1007/s00285-002-0187-1 ...

Stoll, Michael; Yang, Tonghai
On the L-function of the curves y² = x⁵ + A
in Journal of the London Mathematical Society volume 68 (2003) issue 2. - page 273-287
doi:10.1112/S0024610703004460 ...

Stoll, Michael; Cremona, John E.
On the reduction theory of binary forms
in Journal für die Reine und Angewandte Mathematik (2003) issue 565. - page 79-99
doi:10.1515/crll.2003.106 ...

2002

Cremona, John E.; Stoll, Michael
Minimal models for 2-coverings of elliptic curves
in LMS Journal of Computation and Mathematics volume 5 (2002) . - page 220-243
doi:10.1112/S1461157000000760 ...

Stoll, Michael
On the arithmetic of the curves y² = xˡ + A, II
in Journal of Number Theory volume 93 (2002) issue 2. - page 183-206
doi:10.1006/jnth.2001.2727 ...

Stoll, Michael
On the height constant for curves of genus two, II
in Acta Arithmetica volume 104 (2002) issue 2. - page 165-182
doi:10.4064/aa104-2-6 ...

2001

Flynn, E. Victor; Leprévost, Franck; Schaefer, Edward F.; Stein, William A.; Stoll, Michael; Wetherell, Joseph L.
Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus ...
in Mathematics of Computation volume 70 (2001) issue 236. - page 1675-1697
doi:10.1090/S0025-5718-01-01320-5 ...

Stoll, Michael
Implementing 2-descent for Jacobians of hyperelliptic curves
in Acta Arithmetica volume 98 (2001) issue 3. - page 245-277
doi:10.4064/aa98-3-4 ...

1999

Poonen, Bjorn; Stoll, Michael
The Cassels-Tate pairing on polarized abelian varieties
in Annals of Mathematics volume 150 (1999) issue 3. - page 1109-1149
doi:10.2307/121064 ...

Poonen, Bjorn; Stoll, Michael
A local-global principle for densities
Ahlgren, Scott D. ; Andrews, George E. ; Ono, Ken (Hrsg.): Topics in Number Theory : in Honor of B. Gordon and S. Chowla
Boston, MA : Springer US, 1999. - page 241-244 . - (Mathematics and its Applications; 467)
doi:10.1007/978-1-4613-0305-3_16 ...

Stoll, Michael
On the height constant for curves of genus two
in Acta Arithmetica volume 90 (1999) issue 2. - page 183-201
http://matwbn.icm.edu.pl/ksiazki/aa/aa90/aa9026.pd ...

1998

Stoll, Michael
On the arithmetic of the curves y² = xˡ + A and their Jacobians
in Journal für die Reine und Angewandte Mathematik (1998) issue 501. - page 171-189
doi:10.1515/crll.1998.076 ...

Stoll, Michael
On the asymptotics of the growth of 2-step nilpotent groups
in Journal of the London Mathematical Society volume 58 (1998) issue 1. - page 38-48
doi:10.1112/S0024610798006371 ...

Schuster, S.; Stoll, Michael
A simple method to analyze resonators in fish hearing
Elsner Norbert ; Wehner, Rüdiger (eds.): Proceedings of the 26th Göttingen Neurobiology Conference. Vol. 2. Göttingen neurobiology report 1998
Stuttgart : Thieme, 1998. - page 303

1997

Stoll, Michael
Bounds for the length of recurrence relations for convolutions of P-recursive sequences
in European Journal of Combinatorics volume 18 (1997) issue 6. - page 707-712
doi:10.1006/eujc.1996.0123 ...

1996

Stoll, Michael
An example of a simple 2-dimensional abelian variety defined over Q with Mordell-Weil group of ...
in Comptes Rendus de l'Académie des Sciences. Series I volume 322 (1996) issue 9. - page 849-851

Stoll, Michael
Rational and transcendental growth series for the higher Heisenberg groups
in Inventiones Mathematicae volume 126 (1996) issue 1. - page 85-109
doi:10.1007/s002220050090 ...

1995

Stoll, Michael
Regular geodesic languages for 2-step nilpotent groups
Combinatorial and geometric group theory : Edinburgh 1993
Cambridge : Cambridge Univ. Press, 1995. - page 294-299 . - (London Mathematical Society Lecture Note Series; 204)

Stoll, Michael
Construction of semiabelian Galois extensions
in Glasgow Mathematical Journal volume 37 (1995) issue 1. - page 99-104
doi:10.1017/S0017089500030433 ...

Stoll, Michael
Two simple 2-dimensional abelian varieties defined over Q with Mordell-Weil group of rank at le ...
in Comptes Rendus de l'Académie des Sciences. Series I volume 321 (1995) issue 10. - page 1341-1345

1994

Stoll, Michael
Asymptotics of some number theoretic functions and an application to the growth of nilpotent gr ...
Bonn, 1994. - 67 page http://www.mathe2.uni-bayreuth.de/stoll/papers/dis ...
(dissertation, 1993, )

1992

Stoll, Michael
Galois groups overcℚ of some iterated polynomials
in Archiv der Mathematik volume 59 (1992) . - page 239-244
doi:10.1007/BF01197321 ...