Institutionen der Universität Bayreuth
Lehrstuhl Mathematik II (Computeralgebra) - Univ.-Prof. Dr. Michael Stoll

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. Bd. 65 (Dezember 2021) Heft 2 . - S. 191-197.
DOI: https://doi.org/10.7169/facm/1945

Rez.:

MathSciNet

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

Rez.:

AMS MatSciNet

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) . - e6.
DOI: https://doi.org/10.1017/fms.2016.1

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: https://doi.org/10.1112/S1461157009000187

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

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

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: https://doi.org/10.2140/ant.2008.2.859

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

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: https://doi.org/10.1090/S0025-5718-2014-02858-5

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: https://doi.org/10.2140/ant.2010.4.763

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) Heft 632 . - S. 63-84.
DOI: https://doi.org/10.1515/CRELLE.2009.050

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) Heft 615 . - S. 121-155.
DOI: https://doi.org/10.1515/CRELLE.2008.012

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: https://doi.org/10.1112/S1461157000000760

Derickx, Maarten ; Kamienny, Sheldon ; Stein, William ; Stoll, Michael:
Torsion points on elliptic curves over number fields of small degree.
In: Algebra & Number Theory. Bd. 17 (2023) Heft 2 . - S. 267-308.
DOI: https://doi.org/10.2140/ant.2023.17.267

dela Cruz, Romar ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
On the minimum number of minimal codewords.
Bayreuth , 2020 . - 9 S.
DOI: https://doi.org/10.15495/EPub_UBT_00004877

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.

Fu, Hang ; Stoll, Michael:
Elliptic curves with common torsion x-coordinates and hyperelliptic torsion packets.
In: Proceedings of the American Mathematical Society. Bd. 150 (2022) . - S. 5137-5149.
DOI: https://doi.org/10.1090/proc/16102

Rez.:

MathSciNet

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: https://doi.org/10.1112/s0010437x19007693

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: https://doi.org/10.1142/S1793042111004162

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: https://doi.org/10.1112/S1461157010000185

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 2 curves.
In: Mathematics of Computation. Bd. 70 (2001) Heft 236 . - S. 1675-1697.
DOI: https://doi.org/10.1090/S0025-5718-01-01320-5

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: https://doi.org/10.1353/ajm.2014.0005

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.

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: https://doi.org/10.1007/s00285-002-0187-1

Heinlein, Daniel ; Kiermaier, Michael ; Kurz, Sascha ; Wassermann, Alfred:
Tables of subspace codes.
Bayreuth , 2019 . - 44 S.

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: https://doi.org/10.4064/aa180618-9-12

Kiermaier, Michael ; Kurz, Sascha:
Classification of Δ-divisible linear codes spanned by codewords of weight Δ.
Bayreuth , 2023 . - 12 S.
DOI: https://doi.org/10.15495/EPub_UBT_00006857

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. Bd. 91 (2023) . - S. 645-675.
DOI: https://doi.org/10.1007/s10623-022-01118-z

Keller, Timo ; Stoll, Michael:
Exact verification of the strong BSD conjecture for some absolutely simple abelian surfaces.
In: Comptes Rendus Mathématique. Bd. 360 (2022) . - S. 483-489.
DOI: https://doi.org/10.5802/crmath.313

Rez.:

MathSciNet

Kiermaier, Michael ; Kurz, Sascha:
On the lengths of divisible codes.
Bayreuth , 2020 . - 17 S.

Kiermaier, Michael ; Kurz, Sascha:
On the lengths of divisible codes.
Bayreuth , 2019 . - 17 S.

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

Müller, Jan Steffen ; Stoll, Michael:
Canonical heights on genus-2 Jacobians.
In: Algebra & Number Theory. Bd. 10 (2016) Heft 10 . - S. 2153-2234.
DOI: https://doi.org/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. Bd. 19 (2016) . - S. 391-405.
DOI: https://doi.org/10.1112/S1461157016000139

Matev, Tzanko:
Good reduction of 1-motives.
Bayreuth , 2014 . - IX, 115 S.
( Dissertation, 2013 , Universität Bayreuth, Fakultät für Mathematik, Physik und Informatik)

Miller, Robert L. ; Stoll, Michael:
Explicit isogeny descent on elliptic curves.
In: Mathematics of Computation. Bd. 82 (2013) . - S. 513-529.
DOI: https://doi.org/10.1090/S0025-5718-2012-02619-6

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: https://doi.org/10.4007/annals.2014.180.3.7

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: https://doi.org/10.1215/S0012-7094-07-13714-1

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: https://doi.org/10.2307/121064

Poonen, Bjorn ; Stoll, Michael:
A local-global principle for densities.
In: 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: https://doi.org/10.1007/978-1-4613-0305-3_16

Reinke, Bernhard ; Schleicher, Dierk ; Stoll, Michael:
The Weierstrass–Durand–Kerner root finder is not generally convergent.
In: Mathematics of Computation. Bd. 92 (2022) Heft 340 . - S. 839-866.
DOI: https://doi.org/10.1090/mcom/3783

Rez.:

MathSciNet

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: https://doi.org/10.4064/aa180526-12-6

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: https://doi.org/10.4064/aa180416-4-10

Stoll, Michael:
Uniform bounds for the number of rational points on hyperelliptic curves of small Mordell-Weil rank.
In: Journal of the European Mathematical Society. Bd. 21 (2019) Heft 3 . - S. 923-956.
DOI: https://doi.org/10.4171/JEMS/857

Stoll, Michael:
Chabauty without the Mordell-Weil group.
In: Böckle, Gebhard ; Decker, Wolfram ; Malle, Gunter (Hrsg.): Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. - Cham : Springer, 2017 . - S. 623-663
DOI: https://doi.org/10.1007/978-3-319-70566-8_28

Stoll, Michael:
An explicit theory of heights for hyperelliptic Jacobians of genus three.
In: Böckle, Gebhard ; Decker, Wolfram ; Malle, Gunter (Hrsg.): Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. - Cham : Springer, 2017 . - S. 665-715
DOI: https://doi.org/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: https://doi.org/10.1080/10586458.2016.1201443

Stoll, Michael:
Descent and covering collections.
In: Beshaj, Lubjana ; Shaska, Tony ; Zhupa, Eustrat ; NATO (Hrsg.): 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: https://doi.org/10.3233/978-1-61499-520-3-176

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

Stoll, Michael:
Rational points on hyperelliptic curves : recent developments.
In: Computeralgebra-Rundbrief. Bd. 54 (2014) . - S. 10-13.

Stoll, Michael ; van Luijk, Ronald:
Explicit Selmer groups for cyclic covers of P¹.
In: Acta Arithmetica. Bd. 159 (2013) . - S. 133-148.
DOI: https://doi.org/10.4064/aa159-2-4

Stoll, Michael:
Descent on elliptic curves.
In: Belabas, Karim ; Beukers, Frits ; Gaudry, Pierrick ; McCallum, William ; Poonen, Bjorn ; Siksek, Samir ; Stoll, Michael ; Watkins, Mark (Hrsg.): 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: https://doi.org/10.1112/blms/bdr086

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

Stoll, Michael:
Rational points on curves.
In: Journal de Théorie des Nombres de Bordeaux. Bd. 23 (2011) Heft 1 . - S. 257-277.
DOI: https://doi.org/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: https://doi.org/10.4171/GGD/139

Siksek, Samir ; Stoll, Michael:
On a problem of Hajdu and Tengely.
In: 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: https://doi.org/10.1007/978-3-642-14518-6_25

Stoll, Michael:
Rational Points on Curves of Genus 2 : Experiments and Speculations.
In: Johannes A. Buchmann, John Cremona and Michael E. Pohst (editors): Algorithms and Number Theory. - Wadern , 2009 . - 4 S . - (Dagstuhl Seminar Proceedings ; 09221 )

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: https://doi.org/10.4064/aa139-1-5

Stoll, Michael:
How to obtain global information from computations over finite fields.
In: 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 )

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

Stoll, Michael:
Applications of the Mordell-Weil sieve.
In: Oberwolfach Reports. Bd. 4 (2007) Heft 3 . - S. 1967-1970.
DOI: https://doi.org/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: https://doi.org/10.2140/ant.2007.1.349

Stoll, Michael:
Independence of rational points on twists of a given curve.
In: Compositio Mathematica. Bd. 142 (2006) Heft 5 . - S. 1201-1214.
DOI: https://doi.org/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.

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: https://doi.org/10.4064/aa125-1-7

Stoll, Michael:
Finite coverings and rational points.
In: Oberwolfach Reports. Bd. 2 (2005) Heft 3 . - S. 1824-1827.
DOI: https://doi.org/10.4171/OWR/2005/32

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: https://doi.org/10.1090/S0002-9947-03-03366-X

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: https://doi.org/10.1112/S0024610703004460

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

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: https://doi.org/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: https://doi.org/10.4064/aa104-2-6

Stoll, Michael:
Implementing 2-descent for Jacobians of hyperelliptic curves.
In: Acta Arithmetica. Bd. 98 (2001) Heft 3 . - S. 245-277.
DOI: https://doi.org/10.4064/aa98-3-4

Stoll, Michael:
On the height constant for curves of genus two.
In: Acta Arithmetica. Bd. 90 (1999) Heft 2 . - S. 183-201.

Stoll, Michael:
On the arithmetic of the curves y² = xˡ + A and their Jacobians.
In: Journal für die Reine und Angewandte Mathematik. (1998) Heft 501 . - S. 171-189.
DOI: https://doi.org/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: https://doi.org/10.1112/S0024610798006371

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

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

Stoll, Michael:
An example of a simple 2-dimensional abelian variety defined over Q with Mordell-Weil group of rank at least 20.
In: Comptes Rendus de l'Académie des Sciences. Series I. Bd. 322 (1996) Heft 9 . - S. 849-851.

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

Stoll, Michael:
Regular geodesic languages for 2-step nilpotent groups.
In: Duncan, Andrew J. ; Gilbert, N. D. ; Howie, James (Hrsg.): Combinatorial and geometric group theory : Edinburgh 1993. - Cambridge : Cambridge Univ. Press, 1995 . - S. 294-299 . - (London Mathematical Society Lecture Note Series ; 204 )

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

Stoll, Michael:
Two simple 2-dimensional abelian varieties defined over Q with Mordell-Weil group of rank at least 19.
In: Comptes Rendus de l'Académie des Sciences. Series I. Bd. 321 (1995) Heft 10 . - S. 1341-1345.

Stoll, Michael:
Asymptotics of some number theoretic functions and an application to the growth of nilpotent groups.
Bonn , 1994 . - 67 S. - (Bonner mathematische Schriften ; 266 )
( Dissertation, 1993 , Rheinische Friedrich-Wilhelms-Universität zu Bonn)

Stoll, Michael:
Galois groups overcℚ of some iterated polynomials.
In: Archiv der Mathematik. Bd. 59 (1992) . - S. 239-244.
DOI: https://doi.org/10.1007/BF01197321

Vishkautsan, Solomon ; Stoll, Michael:
Quadratic rational functions with a rational periodic critical point of period 3 : with 5 p Appendix by Michael Stoll: Rational points on a curve of genus 6.
In: Journal de Théorie des Nombres de Bordeaux. Bd. 31 (2019) Heft 1 . - S. 49-79.
DOI: https://doi.org/10.5802/jtnb.1068