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Publikationen von Dr. Stephan Elsenhans

Theses:

  1. Diplomarbeit: Stabile Gitter und Tensorprodukte, Göttingen 2001
  2. Dissertation: Mehrdimensionale Kettenbrüche über Funktionenkörpern unter Verwendung affiner Bruhat-Tits-Gebäude, Mathematica Gottingensis Heft 2/ 2006

Papers:

  1. The Diophantine Equation x4 + 2 y4 = z4 + 4 w4 (with J. Jahnel) - An investigation by computer for |x|, |y|, |z|, |w| < 2.5 106, Math. Comp. 75 (2006) 935-940.
  2. The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds (with J. Jahnel), Algorithmic number theory, Lecture Notes in Computer Science 4076, Springer, Berlin 2006, 317-332.
  3. Experiments with general cubic surfaces (with J. Jahnel), in: Tschinkel, Y. and Zarhin, Y. (Eds.): Algebra, Arithmetic, and Geometry, In Honor of Yu. I. Manin, Volume I, Progress in Mathematics 269, Birkhäuser, Boston 2007, 637-654.
  4. On the Smallest Point on a Diagonal Quartic Threefold (with J. Jahnel), Journal of the Ramanujan Mathematical Society 22 (2007)189-204.
  5. K3 surfaces of Picard rank one which are double covers of the projective plane (with J. Jahnel), in: The Higher-dimensional geometry over finite fields, IOS Press, Amsterdam 2008, 63-77.
  6. K3 surfaces of Picard rank one and degree two (with J. Jahnel), in: Algorithmic number theory, Lecture Notes in Computer Science 5011, Springer, Berlin 2008, 212-225.
  7. New sums of three cubes (with J. Jahnel), Math. Comp. 78 (2009) 1227-1230.
  8. Estimates for Tamagawa numbers of diagonal cubic surfaces (with J. Jahnel), Journal of Number Theory 130 (2010) 1835-1853.
  9. Cubic surfaces with a Galois invariant double-six (with J. Jahnel), Central European Journal of Mathematics 8 (2010) 646-661.
  10. On the smallest point on a diagonal cubic surface (with J. Jahnel), Experimental Mathematics 19 (2010) 181-193.
  11. On Weil polynomials of K3 surfaces (with J. Jahnel), in: Algorithmic number theory, Lecture Notes in Computer Science 6197, Springer, Berlin 2010, 126-141.
  12. On the Brauer-Manin obstruction for cubic surfaces (with J. Jahnel), Journal of Combinatorics and Number Theory 2 (2010) 107-128.
  13. Cubic surfaces with a Galois invariant pair of Steiner trihedra (with J. Jahnel), International Journal of Number Theory 7 (2011) 947-970.
  14. On the computation of the Picard group for K3 surfaces (with J. Jahnel), Math. Proc. Camb. Phil. Soc. 151 (2011) 263-270.
  15. Rational points on some Fano quadratic bundles, Experimental Mathematics 20 (2011) 373-379.
  16. The Picard group of a K3 surface and its reduction modulo p (with J. Jahnel), Algebra & Number Theory 5 (2011) 1027-1040.
  17. Rational points on diagonal quartic surfaces, Math. Comp. 81 (2012) 481-492.
  18. Invariants for the Computation of intransitive and transitive Galois Groups, Journal of Symbolic Computation 47 (2012) 315-326.
  19. On the quasi group of a cubic surface over a finite field (with J. Jahnel), Journal of Number Theory 132 (2012) 1554-1571.
  20. On cubic surfaces with a rational line (with J. Jahnel), Archiv der Mathematik 98 (2012) 229-234.
  21. Kummer surfaces and the computation of the Picard group (with J. Jahnel), LMS Journal of Computation and Mathematics 15 (2012) 84-100.
  22. The discriminant of a cubic surface (with J. Jahnel), Geometriae Dedicata 159 (2012) 29-40.
  23. On the order three Brauer classes for cubic surfaces (with J. Jahnel), Central European Journal of Mathematics 10 (2012) 903-926.
  24. On the arithmetic of the discriminant for cubic surfaces (with J. Jahnel), Journal of the Ramanujan Mathematical Society 27 (2012) 355-373.
  25. On the computation of the Picard group for certain singular quartic surfaces (with J. Jahnel), Mathematica Slovaca 63 (2013) 215-228.
  26. On the factor alpha in Peyre's constant (with U. Derenthal, J. Jahnel), Mathematics of Computation 83 (2014) 965-977.
  27. Experiments with the transcendental Brauer-Manin obstruction (with J. Jahnel), in: Proceedings of the ANTS X conference (San Diego 2012), MSP, Berkeley 2013, 369-394.
  28. Examples of K3 surfaces with real multiplication (with J. Jahnel), in: Proceedings of the ANTS XI conference (Gyeongju 2014), LMS Journal of Computation and Mathematics 17 (2014) 14-35.
  29. A note on short cosets, Experimental Mathematics 23 (2014) 411-413.
  30. Explicit computations of invariants of plane quartic curves, Journal of Symbolic Computation 68, Part 2 (2015) 109-115.
  31. Cubic surfaces violating the Hasse principle are Zariski dense in the moduli scheme (with J. Jahnel), Advances in Mathematics 280 (2015) 360-378.
  32. On the characteristic polynomial of the Frobenius on étale cohomology (with J. Jahnel), Duke Mathematical Journal 164 (2015) 2161-2184.
  33. Moduli spaces and the inverse Galois problem for cubic surfaces (with J. Jahnel), Transactions of the AMS 367 (2015) 7837-7861.
  34. Imoroved methods for the construction of relative invariants for permutation groupsJournal of Symbolic Computation, Volume 79, Part 2, March–April 2017, Pages 211–231.

 

Preprints:


  1. On the distribution of the Picard ranks of the reductions of a K3 surface (with Edgar Costa, Jörg Jahnel)
  2. Computing subfields of number fields and applications to Galois group computations (with J. Klueners)
  3. Constructing network codes using Möbius transformations (with A. Kohnert)
  4. Construction of Codes for Network Coding (with A. Kohnert, A. Wassermann)
  5. Good models for cubic surfaces
  6. The Diophantine Equation x4 + 2 y4 = z4 + 4 w4 - A number of improvements (with J. Jahnel)
  7. The Fibonacci sequence modulo p2 - An investigation by computer for p < 1014 (with J. Jahnel)

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