Institutions of the University of Bayreuth
Chair Mathematics II (Computer Algebra) - Univ.-Prof. Dr. Michael Stoll

Kiermaier, Michael ; Kurz, Sascha:
Classification of Δ-divisible linear codes spanned by codewords of weight Δ.
Bayreuth , 2023 . - 12 p.
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. Vol. 91 (2022) . - pp. 645-675.
DOI: https://doi.org/10.1007/s10623-022-01118-z

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

Freitas, Nuno ; Naskręcki, Bartosz ; Stoll, Michael:
The generalized Fermat equation with exponents 2, 3, n.
In: Compositio Mathematica. Vol. 156 (January 2020) Issue 1 . - pp. 77-113.
DOI: https://doi.org/10.1112/s0010437x19007693

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

DeMark, David ; Hindes, Wade ; Jones, Rafe ; Misplon, Moses ; Stoll, Michael ; Stoneman, Michael:
Eventually stable quadratic polynomials over ℚ.
In: New York Journal of Mathematics. Vol. 26 (2020) . - pp. 526-561.

Sawin, Will ; Shusterman, Mark ; Stoll, Michael:
Irreducibility of polynomials with a large gap.
In: Acta Arithmetica. Vol. 192 (2020) Issue 2 . - pp. 111-139.
DOI: https://doi.org/10.4064/aa180526-12-6

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

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

Stoll, Michael:
Diagonal genus 5 curves, elliptic curves over ℚ(t), and rational diophantine quintuples.
In: Acta Arithmetica. Vol. 190 (2019) Issue 3 . - pp. 239-261.
DOI: https://doi.org/10.4064/aa180416-4-10

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. Vol. 31 (2019) Issue 1 . - pp. 49-79.
DOI: https://doi.org/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. Vol. 189 (2019) Issue 3 . - pp. 283-308.
DOI: https://doi.org/10.4064/aa180618-9-12

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. Vol. 21 (2019) Issue 3 . - pp. 923-956.
DOI: https://doi.org/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. Vol. 7 (2019) . - e31.
DOI: https://doi.org/10.1017/fms.2019.20

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

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

Review:

AMS MatSciNet

Stoll, Michael:
Chabauty without the Mordell-Weil group.
In: Böckle, Gebhard ; Decker, Wolfram ; Malle, Gunter (ed.): Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. - Cham : Springer, 2017 . - pp. 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 (ed.): Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory. - Cham : Springer, 2017 . - pp. 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. Vol. 26 (2017) Issue 4 . - pp. 446-459.
DOI: https://doi.org/10.1080/10586458.2016.1201443

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

Müller, Jan Steffen ; Stoll, Michael:
Canonical heights on genus-2 Jacobians.
In: Algebra & Number Theory. Vol. 10 (2016) Issue 10 . - pp. 2153-2234.
DOI: https://doi.org/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. Vol. 4 (2016) . - e6.
DOI: https://doi.org/10.1017/fms.2016.1

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. Vol. 84 (March 2015) Issue 292 . - pp. 895-922.
DOI: https://doi.org/10.1090/S0025-5718-2014-02858-5

Stoll, Michael:
Descent and covering collections.
In: Beshaj, Lubjana ; Shaska, Tony ; Zhupa, Eustrat ; NATO (ed.): 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 . - pp. 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

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

Siksek, Samir ; Stoll, Michael:
The generalised Fermat equation x²+y³=z¹⁵.
In: Archiv der Mathematik. Vol. 102 (May 2014) Issue 5 . - pp. 411-421.
DOI: https://doi.org/10.1007/s00013-014-0639-z

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

Poonen, Bjorn ; Stoll, Michael:
Most odd degree hyperelliptic curves have only one rational point.
In: Annals of Mathematics. Vol. 180 (2014) Issue 3 . - pp. 1137-1166.
DOI: https://doi.org/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. Vol. 136 (2014) Issue 1 . - pp. 77-109.
DOI: https://doi.org/10.1353/ajm.2014.0005

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

Stoll, Michael ; van Luijk, Ronald:
Explicit Selmer groups for cyclic covers of P¹.
In: Acta Arithmetica. Vol. 159 (2013) . - pp. 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 (ed.): 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 . - pp. 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. Vol. 44 (2012) Issue 1 . - pp. 151-166.
DOI: https://doi.org/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. Vol. 2012 (2012) Issue 157 . - pp. 1-41.

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 . - pp. 9-19
DOI: https://doi.org/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. Vol. 7 (2011) Issue 7 . - pp. 1781-1806.
DOI: https://doi.org/10.1142/S1793042111004162

Stoll, Michael:
Rational points on curves.
In: Journal de Théorie des Nombres de Bordeaux. Vol. 23 (2011) Issue 1 . - pp. 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. Vol. 5 (2011) Issue 2 . - pp. 553-565.
DOI: https://doi.org/10.4171/GGD/139

Cremona, John E. ; Fisher, Tom A. ; Stoll, Michael:
Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves.
In: Algebra & Number Theory. Vol. 4 (25 September 2010) Issue 6 . - pp. 763-820.
DOI: https://doi.org/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. Vol. 13 (August 2010) . - pp. 272-306.
DOI: https://doi.org/10.1112/S1461157009000187

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 . - pp. 316-330 . - (Lecture Notes in Computer Science ; 6197 )
DOI: https://doi.org/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. Vol. 13 (2010) . - pp. 451-460.
DOI: https://doi.org/10.1112/S1461157010000185

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

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 )

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 . - pp. 63-84.
DOI: https://doi.org/10.1515/CRELLE.2009.050

Stoll, Michael ; Walsh, P. G. ; Yuan, Pingzhi:
On the Diophantine equation X² - (2²ᵐ + 1) Y⁴ = -2²ᵐ.
In: Acta Arithmetica. Vol. 139 (2009) Issue 1 . - pp. 57-63.
DOI: https://doi.org/10.4064/aa139-1-5

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

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

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 . - pp. 121-155.
DOI: https://doi.org/10.1515/CRELLE.2008.012

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 . - pp. 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. Vol. 2 (2008) Issue 8 . - pp. 859-885.
DOI: https://doi.org/10.2140/ant.2008.2.859

Stoll, Michael:
Applications of the Mordell-Weil sieve.
In: Oberwolfach Reports. Vol. 4 (2007) Issue 3 . - pp. 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. Vol. 1 (2007) Issue 4 . - pp. 349-391.
DOI: https://doi.org/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. Vol. 137 (2007) Issue 1 . - pp. 103-158.
DOI: https://doi.org/10.1215/S0012-7094-07-13714-1

Stoll, Michael:
Independence of rational points on twists of a given curve.
In: Compositio Mathematica. Vol. 142 (September 2006) Issue 5 . - pp. 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. Vol. 6 (2006) Issue 2 . - pp. 359-388.

Stoll, Michael:
On the number of rational squares at fixed distance from a fifth power.
In: Acta Arithmetica. Vol. 125 (2006) Issue 1 . - pp. 79-88.
DOI: https://doi.org/10.4064/aa125-1-7

Stoll, Michael:
Finite coverings and rational points.
In: Oberwolfach Reports. Vol. 2 (2005) Issue 3 . - pp. 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. Vol. 356 (2004) Issue 3 . - pp. 1209-1231.
DOI: https://doi.org/10.1090/S0002-9947-03-03366-X

Geigant, Edith ; Stoll, Michael:
Bifurcation analysis of an orientational aggregation model.
In: Journal of Mathematical Biology. Vol. 46 (2003) Issue 6 . - pp. 537-563.
DOI: https://doi.org/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. Vol. 68 (2003) Issue 2 . - pp. 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) Issue 565 . - pp. 79-99.
DOI: https://doi.org/10.1515/crll.2003.106

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

Stoll, Michael:
On the arithmetic of the curves y² = xˡ + A, II.
In: Journal of Number Theory. Vol. 93 (2002) Issue 2 . - pp. 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. Vol. 104 (2002) Issue 2 . - pp. 165-182.
DOI: https://doi.org/10.4064/aa104-2-6

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. Vol. 70 (2001) Issue 236 . - pp. 1675-1697.
DOI: https://doi.org/10.1090/S0025-5718-01-01320-5

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

Poonen, Bjorn ; Stoll, Michael:
The Cassels-Tate pairing on polarized abelian varieties.
In: Annals of Mathematics. Vol. 150 (November 1999) Issue 3 . - pp. 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 . - pp. 241-244 . - (Mathematics and its Applications ; 467 )
DOI: https://doi.org/10.1007/978-1-4613-0305-3_16

Stoll, Michael:
On the height constant for curves of genus two.
In: Acta Arithmetica. Vol. 90 (1999) Issue 2 . - pp. 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) Issue 501 . - pp. 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. Vol. 58 (1998) Issue 1 . - pp. 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 . - p. 303

Stoll, Michael:
Bounds for the length of recurrence relations for convolutions of P-recursive sequences.
In: European Journal of Combinatorics. Vol. 18 (August 1997) Issue 6 . - pp. 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. Série I. Vol. 322 (1996) Issue 9 . - pp. 849-851.

Stoll, Michael:
Rational and transcendental growth series for the higher Heisenberg groups.
In: Inventiones Mathematicae. Vol. 126 (1996) Issue 1 . - pp. 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 (ed.): Combinatorial and geometric group theory : Edinburgh 1993. - Cambridge : Cambridge Univ. Press, 1995 . - pp. 294-299 . - (London Mathematical Society Lecture Note Series ; 204 )

Stoll, Michael:
Construction of semiabelian Galois extensions.
In: Glasgow Mathematical Journal. Vol. 37 (1995) Issue 1 . - pp. 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. Série I. Vol. 321 (1995) Issue 10 . - pp. 1341-1345.

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

Stoll, Michael:
Galois groups over ℚ of some iterated polynomials.
In: Archiv der Mathematik. Vol. 59 (September 1992) Issue 3 . - pp. 239-244.
DOI: https://doi.org/10.1007/BF01197321