Algebra, Geometry and Computer Algebra Group

Prof. Dr. Claus Fieker

Address

Gottlieb-Daimler-Straße
Gebäude 48, Raum 414
67663 Kaiserslautern

Postfach 3049
67653 Kaiserslautern

Contact

Phone: +49 631 205 2392
Fax: +49 631 205 4427
E-Mail: fieker (at) mathematik.uni-kl.de

Research Interests

  • Algorithmic number theory
  • Constructive class field theory
  • Galois theory
  • (integer) representations of finite groups
  • Computer algebra
  • Jean-François Biasse, Claus Fieker, Tommy Hofmann (2016). On the computation of the HNF of a module over the ring of integers of a number field. JSC. in press, [www] 
  • Jean-François Biasse, Claus Fieker, Mike Jacobson Jr (2016). Fast heuristic algorithms for computing relations in the class group of a quadratic order with applications to isogeny evaluation. LMS J. Comput. Math.. 19A, 371-390. [doi]
  • Janko Böhm, Wolfram Decker, Claus Fieker, Gerhard Pfister (2015). The use of bad primes in rational reconstruction. Math. Comput.. 84, 3013-3027. [doi] 
  • Dereje Kifle Boku and Wolfram Decker and Claus Fieker and Andreas Steenpass (2015). Gröbner Bases over Algebraic Number Fields. ACM ICPS. 16-24. [doi]
  • Claus Fieker (2015). Appendix to Denominators of algebraic numbers in a number field by M. Ayad, A. Bayad and O. Kihel. J. Num. Thy.. 149, 1-14.
  • Claus Fieker, Jürgen Klüners (2014). Computation of Galois groups of rational polynomials. LMS J. Comput. Math.. 17, 141-158. [doi]
  • Claus Fieker, Tommy Hofmann (2014). Computing in quotients of rings of integers. LMS J. Comput. Math.. 17A, 349-365. [doi]
  • Jean-François Biasse, Claus Fieker (2014). Subexponential class group and unit group computation in large deg ree number fields. LMS J. Comput. Math.. 17A, 385-403. [doi] 
  • Fieker, Claus and Gaál, István and Pohst, Michael (2013). On computing integral points of a Mordell curve over rational function fields in characteristic <nobr></nobr>. J. Number Theory. 133, (2), 738--750. (2994384) [doi][www]
  • Claus Fieker, M. M. Gehringer, L. Adler, A. A. Roberts, M. C. Moffitt, T. K. Mihali, T. J. Mills, B. A. Neilan (2012). Nodularin, a cynaobacterial toxin, is synthesized in plants by symbiotic Nostoc sp.. The ISME Journal. (6), 1834-1847. [doi]
  • Claus Fieker and Jean-François Biasse (2012). Improved techniques for computing the ideal class group and the unit group of a number field. Kiran S. Kedlaya (eds.) Proceedings of the ANTS-X conference. Mathematical Science Publishers: (math.ucsd.edu/~kedlaya/ants10/paper-biasse.html)
  • Vincent Ducet, Claus Fieker (2012). Computing equations of curves with many points. Kiran S. Kedlaya (eds.) ANTS-X. MSP - The Open Book Series, Vol 1: 317-334. [www] 
  • Claus Fieker, M. M. Gehringer, J.J. Pengelly, W.S. Cuddy, P.I. Forster, B.A. Neilan (2010). Host selection of symbiotic cyanobacteria in 31 species of the Australian cycad genus: macrozamia (zamiaceae). Mol Plant Microbe Interact. 6, (23), 811-822.
  • Fieker, Claus and Stehlé, Damien (2010). Short bases of lattices over number fields. Algorithmic number theory. Lecture Notes in Comput. Sci. 6197, 157--173. (2721419 (2012d:11247)) [doi][www] 
  • Fieker, Claus (2009). Minimizing representations over number fields. II. Computations in the Brauer group. J. Algebra. 322, (3), 752--765. (2531221 (2010e:20016)) [doi][www]
  • Fieker, Claus and Pohst, Michael E. (2008). A lower regulator bound for number fields. J. Number Theory. 128, (10), 2767--2775. (2441075 (2009k:11181)) [doi][www]
  • Fieker, Claus (2007). Sparse representation for cyclotomic fields. Experiment. Math.. 16, (4), 493--500. (2378488 (2009c:11210)) [www]
  • Fieker, Claus and de Graaf, Willem A. (2007). Finding integral linear dependencies of algebraic numbers and algebraic Lie algebras. LMS J. Comput. Math.. 10, 271--287. (2320832 (2008f:11119))
  • Fieker, Claus (2006). Applications of the class field theory of global fields. Discovering mathematics with Magma. Algorithms Comput. Math. 19, 31--62. (2278922 (2008f:11145)) [doi][www] 
  • Fieker, Claus and Pohst, Michael E. (2006). Dependency of units in number fields. Math. Comp.. 75, (255), 1507--1518 (electronic). (2219041 (2007a:11168)) [doi][www]
  • Fieker, Claus (2004). Minimizing representations over number fields. J. Symbolic Comput.. 38, (1), 833--842. (2094558 (2005g:20023)) [doi][www]
  • Fieker, Claus and Klüners, Jürgen (2003). Minimal discriminants for fields with small Frobenius groups as Galois groups. J. Number Theory. 99, (2), 318--337. (1968456 (2004f:11147)) [doi][www]
  • Claus Fieker and David Kohel (eds.) (2002). ANTS-V. LNCS (2369)
  • Fieker, Claus (2001). Computing class fields via the Artin map. Math. Comp.. 70, (235), 1293--1303 (electronic). (1826583 (2002e:11153)) [doi][www]
  • Fieker, Claus and Friedrichs, Carsten (2000). On reconstruction of algebraic numbers. Algorithmic number theory (Leiden, 2000). Lecture Notes in Comput. Sci. 1838, 285--296. (1850612 (2002g:11181)) [doi][www] 
  • Acciaro, Vincenzo and Fieker, Claus (2000). Finding normal integral bases of cyclic number fields of prime degree. J. Symbolic Comput.. 30, (2), 129--136. (1777167 (2001i:11125)) [doi][www]
  • Daberkow, M. and Fieker, C. and Klüners, J. and Pohst, M. and Roegner, K. and Schörnig, M. and Wildanger, K. (1997). KANT V4. J. Symbolic Comput.. 24, (3-4), 267--283. (1484479 (99g:11150)) (Computational algebra and number theory (London, 1993)) [doi][www]
  • Fieker, C. and Jurk, A. and Pohst, M. (1997). On solving relative norm equations in algebraic number fields. Math. Comp.. 66, (217), 399--410. (1355008 (97c:11118)) [doi][www]
  • Fieker, C. and Pohst, M. E. (1996). On lattices over number fields. Algorithmic number theory (Talence, 1996). Lecture Notes in Comput. Sci. 1122, 133--139. (1446505 (98g:11079)) [doi][www]