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Chair of Computer Algebra – Prof. Dr. Michael Stoll

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Overview
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


Publications

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 page
doi:10.15495/EPub_UBT_00005925 ...

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 ...

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

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

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 volume 7 (2019) . - page 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 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 ...

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

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
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 ...

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
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 ...

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 ...

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) . - page 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 volume 84 (2015) issue 292. - page 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. - 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 ...

2014

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

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 ...

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 ...

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

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 ...

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 ...

2008

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 ...

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 ...

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
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 ...

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 volume 322 (1996) issue 9. - page 849-851

1995

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
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
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 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 over ℚ of some iterated polynomials
in Archiv der Mathematik volume 59 (1992) issue 3. - page 239-244
doi:10.1007/BF01197321 ...

Prof. Dr. Michael Stoll

Fakultät für Mathematik, Physik und Informatik
Mathematisches Institut


Prof. Dr. Michael Stoll
Full Professor

Universität Bayreuth
95440 Bayreuth,

Germany

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

Webmaster: Chair of Computer Algebra

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