Publications Dr. Stephan Elsenhans
Theses:
- Diplomarbeit: Stabile Gitter und Tensorprodukte, Göttingen 2001
- Dissertation: Mehrdimensionale Kettenbrüche über Funktionenkörpern unter Verwendung affiner Bruhat-Tits-Gebäude, Mathematica Gottingensis Heft 2/ 2006
Papers:
- 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.
- 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.
- 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.
- On the Smallest Point on a Diagonal Quartic Threefold (with J. Jahnel), Journal of the Ramanujan Mathematical Society 22 (2007)189-204.
- 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.
- 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.
- New sums of three cubes (with J. Jahnel), Math. Comp. 78 (2009) 1227-1230.
- Estimates for Tamagawa numbers of diagonal cubic surfaces (with J. Jahnel), Journal of Number Theory 130 (2010) 1835-1853.
- Cubic surfaces with a Galois invariant double-six (with J. Jahnel), Central European Journal of Mathematics 8 (2010) 646-661.
- On the smallest point on a diagonal cubic surface (with J. Jahnel), Experimental Mathematics 19 (2010) 181-193.
- On Weil polynomials of K3 surfaces (with J. Jahnel), in: Algorithmic number theory, Lecture Notes in Computer Science 6197, Springer, Berlin 2010, 126-141.
- On the Brauer-Manin obstruction for cubic surfaces (with J. Jahnel), Journal of Combinatorics and Number Theory 2 (2010) 107-128.
- Cubic surfaces with a Galois invariant pair of Steiner trihedra (with J. Jahnel), International Journal of Number Theory 7 (2011) 947-970.
- On the computation of the Picard group for K3 surfaces (with J. Jahnel), Math. Proc. Camb. Phil. Soc. 151 (2011) 263-270.
- Rational points on some Fano quadratic bundles, Experimental Mathematics 20 (2011) 373-379.
- The Picard group of a K3 surface and its reduction modulo p (with J. Jahnel), Algebra & Number Theory 5 (2011) 1027-1040.
- Rational points on diagonal quartic surfaces, Math. Comp. 81 (2012) 481-492.
- Invariants for the Computation of intransitive and transitive Galois Groups, Journal of Symbolic Computation 47 (2012) 315-326.
- On the quasi group of a cubic surface over a finite field (with J. Jahnel), Journal of Number Theory 132 (2012) 1554-1571.
- On cubic surfaces with a rational line (with J. Jahnel), Archiv der Mathematik 98 (2012) 229-234.
- Kummer surfaces and the computation of the Picard group (with J. Jahnel), LMS Journal of Computation and Mathematics 15 (2012) 84-100.
- The discriminant of a cubic surface (with J. Jahnel), Geometriae Dedicata 159 (2012) 29-40.
- On the order three Brauer classes for cubic surfaces (with J. Jahnel), Central European Journal of Mathematics 10 (2012) 903-926.
- On the arithmetic of the discriminant for cubic surfaces (with J. Jahnel), Journal of the Ramanujan Mathematical Society 27 (2012) 355-373.
- On the computation of the Picard group for certain singular quartic surfaces (with J. Jahnel), Mathematica Slovaca 63 (2013) 215-228.
- On the factor alpha in Peyre's constant (with U. Derenthal, J. Jahnel), Mathematics of Computation 83 (2014) 965-977.
- 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.
- 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.
- A note on short cosets, Experimental Mathematics 23 (2014) 411-413.
- Explicit computations of invariants of plane quartic curves, Journal of Symbolic Computation 68, Part 2 (2015) 109-115.
- Cubic surfaces violating the Hasse principle are Zariski dense in the moduli scheme (with J. Jahnel), Advances in Mathematics 280 (2015) 360-378.
- On the characteristic polynomial of the Frobenius on étale cohomology (with J. Jahnel), Duke Mathematical Journal 164 (2015) 2161-2184.
- Moduli spaces and the inverse Galois problem for cubic surfaces (with J. Jahnel), Transactions of the AMS 367 (2015) 7837-7861.
- Point counting on K3 surfaces and an application concerning real and complex multiplication (with J. Jahnel), LMS J. Comput. Math. 19 (2016), suppl. A, 12-28.
- Improved methods for the construction of relative invariants for permutation groups, Journal of Symbolic Computation, Volume 79, Part 2, March–April 2017, Pages 211–231.
- Computing subfields of number fields and applications to Galois group computations, (with J. Klueners) J.Symb.Comput., 93, 2018, 1-20.
Preprints:
- On plane quartics with a Galois invariant Steiner hexad (with Jörg Jahnel)
- On the distribution of the Picard ranks of the reductions of a K3 surface (with Edgar Costa, Jörg Jahnel)
- Computing subfields of number fields and applications to Galois group computations, (with J. Klueners)
- On the construction of relative invariants
- Constructing network codes using Möbius transformations (with A. Kohnert)
- Construction of Codes for Network Coding (with A. Kohnert, A. Wassermann)
- Good models for cubic surfaces
- The Diophantine Equation x4 + 2 y4 = z4 + 4 w4 - A number of improvements (with J. Jahnel)
- The Fibonacci sequence modulo p2 - An investigation by computer for p < 1014 (with J. Jahnel)
- Real and complex multiplication on K3 surfaces via period integration (with J. Jahnel)
- On plane quartics with a Galois invariant Cayley octad (with J. Jahnel)
- Imaginary quadratic number fields with class groups of small exponent (with J. Klueners, F. Nicolae)