Publications of the cosec research group (von zur Gathen, Bonn-Aachen International Center for Information Technology)
Subject area: number theory (sorted by year)
Last generated: 13 May 2012, 03:35.
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2009
Daniel Loebenberger (2009). A Simple Derivation for the Frobenius Pseudoprime Test. In WeWORC 2009. Local PDF (107KB).
2006
Preda Mihăilescu (2006). On the class groups of cyclotomic extensions in presence of a solution to Catalan’s equation. Journal of Number Theory 118(1), 123-144.
2004
Preda Mihăilescu (2004). Primary units and a proof of Catalan’s conjecture. Journal für die reine und angewandte Mathematik 572, 167-195. Link to electronic version.
2003
Preda Mihăilescu (2003). A class number free criterion for Catalan’s conjecture. Journal of Number Theory 99(2), 225-231. ISSN 0022-314X. Link to electronic version.
2001
Eric Bach, Joachim von zur Gathen & Hendrik W. Lenstra, Jr. (2001). Factoring Polynomials over Special Finite Fields. Finite Fields and Their Applications 7, 5-28. Link to PDF version. Local PDF (293KB).
Joachim von zur Gathen & Igor Shparlinski (2001). Gauß Periods in Finite Fields. In Finite Fields and Applications, Dieter Jungnickel & Harald Niederreiter, editors, 162-177. Springer-Verlag. Link to electronic version. Local PDF (316KB).
2000
Joachim von zur Gathen & Francesco Pappalardi (2000). Density estimates for Gauß periods. In Proc. Workshop on Cryptography and Computational Number Theory (CCNT’99, Singapore), K.-Y. Lam, I. E. Shparlinski, H. Wang & C. Xing, editors. Birkhäuser Verlag. Final version in Progress in Computer Science and Applied Logic.
1999
Gene Cooperman, Sandra Feisel, Joachim von zur Gathen & George Havas (1999). GCD of Many Integers. In COCOON ’99, T. Asano, H. Imai, D. T. Lee, S. Nakano & T. Tokuyama, editors, number 1627 in Lecture Notes in Computer Science, 310-317. Springer-Verlag. ISSN 302-9743 (Print) 1611-3349 (Online). Link to electronic version.
Joachim von zur Gathen (1999). Gauß periods. In Abstracts of the Fifth International Conference on Finite Fields and Applications, 1999, University of Augsburg, 29.
1998
Joachim von zur Gathen & Silke Hartlieb (1998). Factoring Modular Polynomials. Journal of Symbolic Computation 26(5), 583-606. Link to electronic version. Extended abstract in von zur Gathen & Hartlieb (1996).
Joachim von zur Gathen & Igor Shparlinski (1998). Orders of Gauss Periods in Finite Fields. Applicable Algebra in Engineering, Communication and Computing 9(1), 15-24. Link to electronic version. Extended abstract in von zur Gathen & Shparlinski (1995). Local PDF (235KB).
Joachim von zur Gathen & Igor Shparlinski (1998). The CREW PRAM complexity of modular inversion. In Proceedings of LATIN ’98, Campinas, Brazil, C. L. Lucchesi & A. V. Moura, editors, number 1380 in Lecture Notes in Computer Science, 305-315. Springer-Verlag, Berlin, Heidelberg. ISBN 3-540-64275-7. ISSN 0302-9743. Link to electronic version. Final version in SIAM Journal on Computing. Local PDF (262KB).
1997
Preda Mihăilescu (1997). Cyclotomy of Rings & Primality Testing. Ph.D. thesis, Swiss Federal Institute of Technology, Zürich, Switzerland. Author’s homepage.
1996
Joachim von zur Gathen & Silke Hartlieb (1996). Factoring Modular Polynomials. In Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation ISSAC ’96, Zürich, Switzerland, Lakshman Y. N., editor, 10-17. ACM Press. Link to electronic version. Final version see von zur Gathen & Hartlieb (1998). Local PDF (349KB).
S. Schlink (1996). Normalbasen mit Hilfe von verallgemeinerten Gauß-Perioden. Diplomarbeit, Universität-GH Paderborn, Paderborn.
1995
Joachim von zur Gathen & Igor E. Shparlinski (1995). Orders of Gauss Periods in Finite Fields. In Proceedings of 6th International Symposium on Algorithms and Computation ISAAC ’95, Cairns, Australia, J. Staples, P. Eades, N. Katoh & A. Moffat, editors, number 1004 in Lecture Notes in Computer Science, 208-215. Springer-Verlag, Berlin, Heidelberg. ISBN 3-540-60573-8. ISSN 0302-9743. Link to electronic version. Final version in von zur Gathen & Shparlinski (1998a).
1991
Joachim von zur Gathen (1991). Tests for permutation polynomials. SIAM Journal on Computing 20(3), 591-602. Link to electronic version.
Joachim von zur Gathen (1991). Values of polynomials over finite fields. Bulletin of the Australian Mathematical Society 43, 141-146. Link to electronic version.
1990
Joachim von zur Gathen (1990). Polynomials over finite fields with large images. In Proceedings of the 1990 International Symposium on Symbolic and Algebraic Computation ISSAC ’90, Tokyo, Japan, 140-144. ACM Press. Link to electronic version. Final version in Bulletin of the Australian Mathematical Society.
J. von zur Gathen & M. Giesbrecht (1990). Constructing Normal Bases in Finite Fields. Journal of Symbolic Computation 10, 547-570. ISSN 0747-7171. Link to electronic version.
1987
Joachim von zur Gathen (1987). Factoring polynomials and primitive elements for special primes. Theoretical Computer Science 52, 77-89. Link to electronic version.