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Prof. Dr. Michael Stoll Prof. Dr. Michael Stoll
Prof. Dr. Michael Stoll

Fakultät für Mathematik, Physik und Informatik
Mathematisches Institut


Ordentliches Mitglied der Sektion III der Bayerischen Akademie der Wissenschaften

 

 

Prof. Dr. Michael Stoll

Fakultät für Mathematik, Physik und Informatik
Mathematisches Institut


Publikationen

2020

Kiermaier, Michael; Kurz, Sascha; Solé, Patrick; Stoll, Michael; Wassermann, Alfred
On strongly walk regular graphs,triple sum sets and their codes
Bayreuth, 2020. - 33 S.
doi:10.15495/EPub_UBT_00005192 ...

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

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

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

2019

Checcoli, Sara; Veneziano, Francesco; Viada, Evelina; Stoll, Michael
The explicit Mordell conjecture for families of curves : (with an appendix by M. Stoll)
In: Forum of Mathematics. Sigma Bd. 7 (2019) . - S. e31
doi:10.1017/fms.2019.20 ...

Stoll, Michael
Diagonal genus 5 curves, elliptic curves over ℚ(t), and rational diophantine quintuples
In: Acta Arithmetica Bd. 190 (2019) Heft 3. - S. 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 Bd. 31 (2019) Heft 1. - S. 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 Bd. 189 (2019) Heft 3. - S. 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 Bd. 21 (2019) Heft 3. - S. 923-956
doi:10.4171/JEMS/857 ...

2018

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

2017

Bauer, Ingrid; Stoll, Michael
Geometry and arithmetic of primary Burniat surfaces
In: Mathematische Nachrichten Bd. 290 (2017) Heft 14–15. - S. 2132-2153
doi:10.1002/mana.201600282 ...

Stoll, Michael
Chabauty without the Mordell-Weil group
Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory
Cham : Springer, 2017. - S. 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. - S. 665-715
doi:10.1007/978-3-319-70566-8_29 ...

Stoll, Michael
Simultaneous torsion in the Legendre family
In: Experimental Mathematics Bd. 26 (2017) Heft 4. - S. 446-459
doi:10.1080/10586458.2016.1201443 ...

2016

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

Müller, Jan Steffen; Stoll, Michael
Canonical heights on genus-2 Jacobians
In: Algebra & Number Theory Bd. 10 (2016) Heft 10. - S. 2153-2234
doi:10.2140/ant.2016.10.2153 ...

Bruin, Nils; Poonen, Bjorn; Stoll, Michael
Generalized explicit descent and its application to curves of genus 3
In: Forum of Mathematics, Sigma Bd. 4 (2016) . - S. e6
doi:10.1017/fms.2016.1 ...

2015

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 Bd. 84 (2015) Heft 292. - S. 895-922
doi:10.1090/S0025-5718-2014-02858-5 ...

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. - S. 176-193 . - (NATO Science for Peace and Security : Series D, Information and Communication Security; 41)
doi:10.3233/978-1-61499-520-3-176 ...

2014

Siksek, Samir; Stoll, Michael
The generalised Fermat equation x²+y³=z¹⁵
In: Archiv der Mathematik Bd. 102 (2014) Heft 5. - S. 411-421
doi:10.1007/s00013-014-0639-z ...

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

Poonen, Bjorn; Stoll, Michael
Most odd degree hyperelliptic curves have only one rational point
In: Annals of Mathematics Bd. 180 (2014) Heft 3. - S. 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 Bd. 136 (2014) Heft 1. - S. 77-109
doi:10.1353/ajm.2014.0005 ...

2013

Miller, Robert L.; Stoll, Michael
Explicit isogeny descent on elliptic curves
In: Mathematics of Computation Bd. 82 (2013) . - S. 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 Bd. 159 (2013) . - S. 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. - S. 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 Bd. 44 (2012) Heft 1. - S. 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 Bd. 2012 (2012) Heft 157. - S. 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. - S. 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 Bd. 7 (2011) Heft 7. - S. 1781-1806
doi:10.1142/S1793042111004162 ...

Stoll, Michael
Rational points on curves
In: Journal de Théorie des Nombres de Bordeaux Bd. 23 (2011) Heft 1. - S. 257-277
doi:10.5802/jtnb.760 ...

Stoll, Michael
Reduction theory of point clusters in projective space
In: Groups, Geometry, and Dynamics Bd. 5 (2011) Heft 2. - S. 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 Bd. 4 (2010) Heft 6. - S. 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 Bd. 13 (2010) . - S. 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. - S. 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 Bd. 13 (2010) . - S. 451-460
doi:10.1112/S1461157010000185 ...

2009

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

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 Bd. 632 (2009) . - S. 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 Bd. 139 (2009) Heft 1. - S. 57-63
doi:10.4064/aa139-1-5 ...

2008

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

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 Bd. 615 (2008) . - S. 121-155
doi:10.1515/CRELLE.2008.012 ...

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

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. - S. 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 Bd. 2 (2008) Heft 8. - S. 859-885
doi:10.2140/ant.2008.2.859 ...

2007

Stoll, Michael
Applications of the Mordell-Weil sieve
In: Oberwolfach Reports Bd. 4 (2007) Heft 3. - S. 1967-1970
doi:10.4171/OWR/2007/34 ...

Stoll, Michael
Finite descent obstructions and rational points on curves
In: Algebra & Number Theory Bd. 1 (2007) Heft 4. - S. 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 Bd. 137 (2007) Heft 1. - S. 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 Bd. 142 (2006) Heft 5. - S. 1201-1214
doi:10.1112/S0010437X06002168 ...

Schleicher, Dierk; Stoll, Michael
An introduction to Conway’s games and numbers
In: Moscow Mathematical Journal Bd. 6 (2006) Heft 2. - S. 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 Bd. 125 (2006) Heft 1. - S. 79-88
doi:10.4064/aa125-1-7 ...

2005

Stoll, Michael
Finite coverings and rational points
In: Oberwolfach Reports Bd. 2 (2005) Heft 3. - S. 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 Bd. 356 (2004) Heft 3. - S. 1209-1231
doi:10.1090/S0002-9947-03-03366-X ...

2003

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

Geigant, Edith; Stoll, Michael
Bifurcation analysis of an orientational aggregation model
In: Journal of Mathematical Biology Bd. 46 (2003) Heft 6. - S. 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 Bd. 68 (2003) Heft 2. - S. 273-287
doi:10.1112/S0024610703004460 ...

2002

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

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

Stoll, Michael
On the height constant for curves of genus two, II
In: Acta Arithmetica Bd. 104 (2002) Heft 2. - S. 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 Bd. 70 (2001) Heft 236. - S. 1675-1697
doi:10.1090/S0025-5718-01-01320-5 ...

Stoll, Michael
Implementing 2-descent for Jacobians of hyperelliptic curves
In: Acta Arithmetica Bd. 98 (2001) Heft 3. - S. 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 Bd. 150 (1999) Heft 3. - S. 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. - S. 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 Bd. 90 (1999) Heft 2. - S. 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 Bd. 501 (1998) . - S. 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 Bd. 58 (1998) Heft 1. - S. 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. - S. 303

1997

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

1996

Stoll, Michael
Rational and transcendental growth series for the higher Heisenberg groups
In: Inventiones Mathematicae Bd. 126 (1996) Heft 1. - S. 85-109
doi:10.1007/s002220050090 ...

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. Série I Bd. 322 (1996) Heft 9. - S. 849-851

1995

Stoll, Michael
Construction of semiabelian Galois extensions
In: Glasgow Mathematical Journal Bd. 37 (1995) Heft 1. - S. 99-104
doi:10.1017/S0017089500030433 ...

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

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. Série I Bd. 321 (1995) Heft 10. - S. 1341-1345

1994

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

1992

Stoll, Michael
Galois groups over ℚ of some iterated polynomials
In: Archiv der Mathematik Bd. 59 (1992) Heft 3. - S. 239-244
doi:10.1007/BF01197321 ...

Prof. Dr. Michael Stoll

Fakultät für Mathematik, Physik und Informatik
Mathematisches Institut


Prof. Dr. Michael Stoll
Lehrstuhlinhaber

Universität Bayreuth
95440 Bayreuth,

Germany

Telefon: +49-(0)921-55 3387
E-Mail: Michael.Stoll@uni-bayreuth.de
Homepage: Homepage

Verantwortlich für die Redaktion: Lehrstuhl für Computeralgebra

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