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Computer Algebra

Publications

Publications of Stephan Elsenhans

  • Elsenhans, Andreas-Stephan: Improved methods for the construction of relative invariants for permutation groups.. In: J. Symb. Comput. Bd. 79, Elsevier (Academic Press), London (2017), S. 211-231
     
  • Elsenhans, Andreas-Stephan: Computation of Galois groups in Magma. In: Mathematical and computational approaches in advancing modern science and engineering. Based on the international conference on applied mathematics, modeling and computational science, AMMCS, jointly held with the annual meeting of the Canadian applied and industrial mathematics, CAIMS, June 7--15, 2015 : Cham: Springer, 2016 — ISBN 978-3-319-30377-2/hbk; 978-3-319-30379-6/ebook, S. 621--628
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: Point counting on K3 surfaces and an application concerning real and complex multiplication.. In: LMS J. Comput. Math. Bd. 19A, Cambridge University Press, Cambridge; London Mathematical Society, London (2016), S. 12--28
     
  • Elsenhans, Andreas-Stephan: Explicit computations of invariants of plane quartic curves.. In: J. Symb. Comput. Bd. 68, Elsevier (Academic Press), London (2015), S. 109--115
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: Cubic surfaces violating the Hasse principle are Zariski dense in the moduli scheme.. In: Adv. Math. Bd. 280, Elsevier (Academic Press), San Diego, CA (2015), S. 360--378
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: On the characteristic polynomial of the Frobenius on étale cohomology.. In: Duke Math. J. Bd. 164, Duke University Press, Durham, NC; University of North Carolina, Chapel Hill, NC (2015), Nr. 11, S. 2161--2184
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: Moduli spaces and the inverse Galois problem for cubic surfaces.. In: Trans. Am. Math. Soc. Bd. 367, American Mathematical Society (AMS), Providence, RI (2015), Nr. 11, S. 7837--7861
     

  • Derenthal, Ulrich ; Elsenhans, Andreas-Stephan ; Jahnel, Jörg: On the factor alpha in Peyre's constant.. In: Math. Comput. Bd. 83, American Mathematical Society (AMS), Providence, RI (2014), Nr. 286, S. 965--977
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: Examples of \($K3$\) surfaces with real multiplication.. In: LMS J. Comput. Math. Bd. 17A, Cambridge University Press, Cambridge; London Mathematical Society, London (2014), S. 14--35
     
  • Elsenhans, Andreas-Stephan: A note on short cosets.. In: Exp. Math. Bd. 23, Taylor & Francis, Philadelphia, PA (2014), Nr. 4, S. 411--413
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: On the computation of the Picard group for certain singular quartic surfaces.. In: Math. Slovaca Bd. 63, Slovak Academy of Sciences, Mathematical Institute, Bratislava; De Gruyter (Sciendo), Warsaw (2013), Nr. 2, S. 215--228
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: Experiments with the transcendental Brauer-Manin obstruction. In: ANTS X. Proceedings of the tenth algorithmic number theory symposium, San Diego, CA, USA, July 9--13, 2012 : Berkeley, CA: Mathematical Sciences Publishers (MSP), 2013 — ISBN 978-1-935107-00-2/hbk; 978-1-935107-01-9/ebook, S. 369--394
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: On the arithmetic of the discriminant for cubic surfaces.. In: J. Ramanujan Math. Soc. Bd. 27, Ramanujan Mathematical Society, Mysore, Karnataka, India (2012), Nr. 3, S. 355--373
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: On the order three Brauer classes for cubic surfaces.. In: Cent. Eur. J. Math. Bd. 10, Springer, Heidelberg; De Gruyter Open, Warsaw (2012), Nr. 3, S. 903--926
     
  • Elsenhans, Andreas-Stephan: Invariants for the computation of intransitive and transitive Galois groups.. In: J. Symb. Comput. Bd. 47, Elsevier (Academic Press), London (2012), Nr. 3, S. 315-326
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: On cubic surfaces with a rational line.. In: Arch. Math. Bd. 98, Springer (Birkhäuser), Basel (2012), Nr. 3, S. 229--234
     
  • Elsenhans, Andreas-Stephan: Rational points on diagonal quartic surfaces.. In: Math. Comput. Bd. 81, American Mathematical Society (AMS), Providence, RI (2012), Nr. 277, S. 481--492
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: The discriminant of a cubic surface.. In: Geom. Dedicata Bd. 159, Springer Netherlands, Dordrecht (2012), S. 29--40
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: Kummer surfaces and the computation of the Picard group.. In: LMS J. Comput. Math. Bd. 15, Cambridge University Press, Cambridge; London Mathematical Society, London (2012), S. 84--100
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: On the quasi-group of a cubic surface over a finite field.. In: J. Number Theory Bd. 132, Elsevier (Academic Press), San Diego, CA (2012), Nr. 7, S. 1554--1571
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: Cubic surfaces with a Galois invariant pair of Steiner trihedra.. In: Int. J. Number Theory Bd. 7, World Scientific, Singapore (2011), Nr. 4, S. 947--970
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: The Picard group of a \($K3$\) surface and its reduction modulo \($p$\).. In: Algebra Number Theory Bd. 5, Mathematical Sciences Publishers (MSP), Berkeley, CA (2011), Nr. 8, S. 1027-1040
     
  • Elsenhans, Andreas-Stephan: Rational points on some Fano quadratic bundles.. In: Exp. Math. Bd. 20, Taylor & Francis, Philadelphia, PA (2011), Nr. 4, S. 373--379
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: On the computation of the Picard group for \($K3$\) surfaces.. In: Math. Proc. Camb. Philos. Soc. Bd. 151, Cambridge University Press, Cambridge (2011), Nr. 2, S. 263--270
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: On the smallest point on a diagonal cubic surface.. In: Exp. Math. Bd. 19, Taylor & Francis, Philadelphia, PA (2010), Nr. 2, S. 181--193
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: Estimates for Tamagawa numbers of diagonal cubic surfaces.. In: J. Number Theory Bd. 130, Elsevier (Academic Press), San Diego, CA (2010), Nr. 8, S. 1835--1853
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: On Weil polynomials of \($K3$\) surfaces. In: Algorithmic number theory. 9th international symposium, ANTS-IX, Nancy, France, July 19--23, 2010. Proceedings : Berlin: Springer, 2010 — ISBN 978-3-642-14517-9/pbk, S. 126--141
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: Cubic surfaces with a Galois invariant double-six.. In: Cent. Eur. J. Math. Bd. 8, Springer, Heidelberg; De Gruyter Open, Warsaw (2010), Nr. 4, S. 646--661
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: On the Brauer-Manin obstruction for cubic surfaces.. In: J. Comb. Number Theory Bd. 2, Nova Science Publishers, Hauppauge, NY (2010), Nr. 2, S. 107--128
     

  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: Experiments with general cubic surfaces. In: Algebra, arithmetic, and geometry. In honor of Yu. I. Manin on the occasion of his 70th birthday. Vol. I : Boston, MA: Birkhäuser, 2009 — ISBN 978-0-8176-4744-5/hbk; 978-0-8176-4745-2/ebook, S. 637--653
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: New sums of three cubes.. In: Math. Comput. Bd. 78, American Mathematical Society (AMS), Providence, RI (2009), Nr. 266, S. 1227--1230
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: {\($K3$\) surfaces of Picard rank one and degree two. In: Algorithmic number theory. 8th international symposium, ANTS-VIII Banff, Canada, May 17--22, 2008 Proceedings : Berlin: Springer, 2008 — ISBN 978-3-540-79455-4/pbk, S. 212--225
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: {\($K3$\) surfaces of Picard rank one which are double covers of the projective plane. In: Higher-dimensional geometry over finite fields. Proceedings of the NATO Advanced Study Institute held at the University of Göttingen, Göttingen, Germany, June 25--July 6, 2007 : Amsterdam: IOS Press, 2008 — ISBN 978-1-58603-855-7/hbk, S. 63--77
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: On the smallest point on a diagonal quartic threefold.. In: J. Ramanujan Math. Soc. Bd. 22, Ramanujan Mathematical Society, Mysore, Karnataka, India (2007), Nr. 2, S. 189-204
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds. In: Algorithmic number theory. 7th international symposium, ANTS-VII, Berlin, Germany, July 23--28, 2006. Proceedings., Lecture Notes in Computer Science : Berlin: Springer, 2006 — ISBN 3-540-36075-1, S. 317-332
     
  • Elsenhans, Andreas-Stephan ; Jahnel, Jörg: The Diophantine equation \($ x\sp4 + 2 y\sp4 = z\sp4 + 4 w\sp4$\).}. In: Math. Comput. Bd. 75, American Mathematical Society (AMS), Providence, RI (2006), Nr. 254, S. 935--940
     
  • Elsenhans, Andreas-Stephan: Mehrdimensionale Kettenbrüche über Funktionenkörpern unter Verwendung der Bruhat-Tits-Gebäude. : Göttingen: Univ. Göttingen, Mathematisch-Naturwissenschaftliche Fakultäten (Dissertation), 2005
     
  • Elsenhans, A.-S. ; Jahnel, J.: The Diophantine equation \($x^4+ 2y^4= z^4+ 4w^4$\). In: Mathematisches Institut, Georg-August-Universität Göttingen: Seminars Winter Term 2004/2005. Lecture notes from the seminars ``Number theory'', ``Algebraic geometry'' and ``Twisted cohomology theories'' held at the University of Göttingen, Göttingen, Germany, 2004 : Göttingen: Universitätsverlag Göttingen, 2005 — ISBN 3-938616-17-2/pbk, S. 203--209