Publications

Books

• Wieb Bosma, John Cannon (eds)
  Discovering Mathematics with Magma
  Algorithms and Computation in Mathematics 19
  Berlin: Springer Verlag, 2006.

• Wieb Bosma (ed.)
  Algorithmic Number Theory
  Proceedings 4th International Symposium ANTS-IV, (Leiden, July 2000), Lecture Notes in Computer Science 1838
  Berlin: Springer 2000.

• Wieb Bosma, Alf van der Poorten (eds)
  Computational Algebra and Number Theory
  Mathematics and its Applications 325 Dordrecht: Kluwer, 1995, pp. 321.
  MR 96c:00019

Other Major Works

• Wieb Bosma, John Cannon
  Handbook of Magma functions
  Sydney 1993-2008.

• Wieb Bosma
  RWCA'04, 9th Rhine Workshop Computer Algebra 2004, Proceedings
  Universiteit van Nijmegen, 2004, pp. 144

• Wieb Bosma, M.P.M. van der Hulst
  Primality proving with cyclotomy, Ph.D. Thesis
  Universiteit van Amsterdam, 1990, pp. 337

Recent preprints

• Wieb Bosma, David Gruenewald
  Complex numbers with bounded partial quotients, accepted by the Journal of the Australian Mathematical Society.

• Wieb Bosma, Ionica Smeets
  Finding simultaneous Diophantine approximations with prescribed quality

• Wieb Bosma, Antal Jarai, Gyongyver Kiss
  Better paths for elliptic primality proofs
  Report 0902, Mathematics Department, Radboud University Nijmegen, 2009.

Papers

• Wieb Bosma, Ben Kane
  preprint and final version of The triangular theorem of eight, accepted by the Proceedings of the American Mathematical Society, 2011.

• Wieb Bosma, Ben Kane
  preprint and final version of The aliquot constant, as accepted by the The quarterly journal of mathematics, published online December 23, 2010.

• Wieb Bosma
  Some computational experiments in number theory
  in: Wieb Bosma, John Cannon (eds), Discovering Mathematics with Magma, Algorithms and Computation in Mathematics 19, Berlin: Springer Verlag, 2006
  pp. 1-30

• Wieb Bosma, Karma Dajani, Cor Kraaikamp
  Entropy quotients and correct digits in number-theoretic expansions
  in: IMS Lecture Notes--Monograph Series 48, Dynamics and Stochastics, 2006
  pp. 176-188.

• Wieb Bosma,
  Cubic reciprocity and explicit primality tests for h3^k+-1
  in: Alf van der Poorten, Andreas Stein (eds.), High primes and misdemeanours: lectures in honour of the 60th birthday of Hugh Cowie Williams,
  Fields Inst. Commun., 41, Providence: Amer. Math. Soc. 2004
  pp. 77--89

  extended preprint version:
  Cubic reciprocity and explicit primality tests for h3^k+-1
  Department of Mathematics, Universiteit van Nijmegen, report 05.15, 2005, pp. 1--19

• Wieb Bosma, James Hutton, Eric R. Verheul
  Looking beyond XTR
  in: Y. Zheng (ed.), Advances in Cryptology ASIACRYPT 2002, 8th International Conference on the Theory and Application of Cryptology and Information Security, Queenstown, New Zealand, December 1-5, 2002, Proceedings; Lecture Notes in Computer Science 2501, Springer, 2002
  pp. 46--63

• Wieb Bosma, Bart de Smit
  On arithmetically equivalent number fields of small degree
  in: Claus Fieker, David R. Kohel (eds.), Proceedings of the 5th Algorithmic Number Theory Symposium, Sydney, Australia, July 2002; Lecture Notes in Computer Science 2369 Springer 2002
  pp. 67--79

• Wieb Bosma
  Signed bits and fast exponentiation
  Journal de Théorie des Nombres de Bordeaux, 13 (2001), 27--41.
  MR2002e:11184

  preprint version:
  Signed bits and fast exponentiation
  Department of Mathematics, Universiteit van Nijmegen, report 9935, 1999, pp. 1--15

• Wieb Bosma, Bart de Smit
  Class number relations from a computational point of view
  Journal of Symbolic Computation 31 (2001), 97--112.
  MR2002a:11144

• Wieb Bosma, John Cannon, Allan Steel
  Lattices of compatibly embedded finite fields
  Journal of Symbolic Computation 24} (1997), 351--369.
  MR99a:11143

• Wieb Bosma, John Cannon, Catherine Playoust
  The Magma Algebra System I: The User Language
  Journal of Symbolic Computation 24 (1997), 235--265
  MR 99a:11143

• Wieb Bosma, Peter Stevenhagen
  On the computation of quadratic 2-class groups
  Journal de Théorie des Nombres de Bordeaux8 (1996), 283--313
  MR 98e:11129a
  Erratum:
  Journal de Théorie des Nombres 9 (1997), 1
  MR 98e:11129b

• Wieb Bosma, P. Stevenhagen
  Density computations for real quadratic units
  Math. Comp. 65 (1996), 1327--1337.
  MR 96j:11171

• D. Bleichenbacher, W. Bosma, A.K. Lenstra
  Some remarks on Lucas-based cryptosystems
  in: Don Coppersmith (ed.), Advances in Cryptology Proceedings of Crypto'95, Lecture Notes in Computer Science 963, Springer 1995
  pp. 386--396
  MR 97m:94012

• Wieb Bosma
  Computation of cyclotomic polynomials with Magma
  pp. 213--226 in [A1], 1995.
  MR 96j:11142

• Wieb Bosma, A.K. Lenstra
  An implementation of the elliptic curve integer factorization method, pp. 119--136 in [A1], 1995.
  MR 96d11134

• Wieb Bosma, H.W. Lenstra, Jr.
  Complete systems of two addition laws for elliptic curves
  J. Number Theory 53 (1995), 229--240.
  MR 96f:11079

• Wieb Bosma, P. Stevenhagen
  Density computations for real quadratic 2-class groups
  abstract, in: L.M. Adleman, Ming-Deh Huang, Proceedings of the First Algorithmic Number Theory Symposium, Ithaca, New York, 1994 pp. 17.
  MR1322706

• Wieb Bosma, Graham Matthews, John Cannon
  Programming with algebraic structures: design of the Magma language
  in: M. Giesbrecht (ed), Proceedings of International Symposium on Symbolic and Algebraic Computation, Oxford (1994) Association for Computing Machinery, 1994
  pp. 52--57

• Wieb Bosma
  Explicit primality criteria for h2^k+-1}
  Math. Comp. 61 (D.H. Lehmer memorial issue) (1993), 97--109
  MR 94c:11005

• Wieb Bosma, John Cannon
  Structural Computation in Finite Permutation Groups
  CWI-Quarterly, 5, 2, (1992), 127--160
  MR 93i:20003

• Wieb Bosma, M. Pohst
  Computations with finitely generated modules over Dedekind domains
  in: S.M. Watt (ed), Proceedings of the International Symposium on Symbolic and Algebraic Computation, Bonn (1991), Association for Computing Machinery 1991
  pp. 151--156

• Wieb Bosma, Cor Kraaikamp
  Optimal approximation by continued fractions
  J. Austral. Math. Soc. (Series A), 50 (1991), 481--504
  MR 92f:11093

• Wieb Bosma
  Canonical bases for cyclotomic fields
  Applicable Algebra in Engineering, Communication and Computing 1 (1990), 125--134
  MR 95k:11135

• Wieb Bosma, Cor Kraaikamp
  Metrical theory for optimal continued fractions
  J. Number Theory 34 (1990), 251--270
  MR 91d:11095

• Wieb Bosma, M.P.M. van der Hulst
  Faster primality testing
  in: G. Goos, J. Hartmanis (eds), Advances in cryptology EUROCRYPT '89, Lecture Notes in Computer Science 434, Berlin: Springer 1990
  pp. 652--656

• Wieb Bosma
  Approximation by mediants
  Math. Comp. 54 (1990), 421--434
  MR 90m: 11119

• Wieb Bosma
  Notes on primality testing and factoring
  Prépublication 89-32 (1989), Laboratoire de Mathématiques Marseille.

• Wieb Bosma
  Optimal continued fractions
  Indag. Math. 49 (1987), 353--379
  MR 89b: 40001

• Wieb Bosma, H. Jager and F. Wiedijk
  Some metrical observations on the approximation by continued fractions
  Indag. Math. 45 (1983), 281--299
  MR 85f:11059

• Wieb Bosma
  Primality testing with elliptic curves
  Doctoraalscriptie
  Report 85--12, Department of Mathematics, University of Amsterdam 1985.

Educational and popular

• Wieb Bosma, Jaap Top
  De P van primaliteit
  Nieuw Archief voor Wiskunde (5) 4 no. 1, maart 2003, 43--45.

• Wieb Bosma
  De kwadratische zeef
  Pythagoras 37 nr. 6, augustus 1998, 6--11.
• Jan van de Craats, Wieb Bosma
  Hoe werkt RSA?
  Pythagoras 37 nr. 5, juni 1998, 22--25.
• Wieb Bosma
  Priem of niet?
  Pythagoras 37 nr. 3, februari 1998, 21--23.
• Wieb Bosma
  Modulair rekenen
  Pythagoras 37 nr. 2, december 1997, 24--25.
• Wieb Bosma
  De zeef van Eratosthenes
  Pythagoras 37 nr. 1, oktober 1997, 23--26.

Reports

• Wieb Bosma, Metrical theory for optimal continued fractions, Report 87--11 (1987), Department of Mathematics, University of Amsterdam.
• Wieb Bosma, Optimal continued fractions, Report 87--12 (1987), Department of Mathematics, University of Amsterdam.
• Wieb Bosma, Cor Kraaikamp, Properties of optimal continued fractions, Report 88--09 (1988), Department of Mathematics, University of Amsterdam.
• Wieb Bosma, P. Stevenhagen, Density computations for real quadratic units, Report 94--20 (1994), 1--11.
• Wieb Bosma, P. Stevenhagen, On the computation of quadratic 2-class groups, Report 95--04 (1995), 1--16.
• W. Bosma, K. Dajani and C. Kraaikamp Entropy and Relative Growth of Sequences
  Preprint 1084, Department of Mathematics, Utrecht University, 1998.
• W. Bosma, K. Dajani, C Kraaikamp, Entropy and counting correct digits
  report 9925 Mathematical Institute, University of Nijmegen, June 1999.
• W. Bosma, Signed bits and fast exponentiation
  report 9935 Mathematical Institute, University of Nijmegen, July 1999.
• W. Bosma, B. de Smit, A computational approach to class number relations
  Report MI 1999-27, Mathematisch Instituut, Universiteit Leiden, october 1999.
• Wieb Bosma, Cubic reciprocity and explicit primality tests for h3^k+-1, report 05.15, Department of Mathematics, University of Nijmegen, 2005.
• Wieb Bosma, Some computational experiments in number theory
  report 05.16 Department of Mathematics, University of Nijmegen, 2005.