List of publications

• A transfinite generalization of a combinatorial problem on abelian groups (with P. van Emde Boas), Report WN-29, Mathematisch Centrum, Amsterdam.

• Rational functions invariant under a finite abelian group, Report 72-02, Mathematisch Instituut, Universiteit van Amsterdam.
• Two theorems on perfect codes, Discrete Math. 3, 125–132.

• Simple abelian varieties having a prescribed formal isogeny type (with F. Oort), Report 73-02, Mathematisch Instituut, Universiteit van Amsterdam.
• Multiplicative division algorithms on the integers (with A. E. Brouwer), Report 54/73, Mathematisch Centrum, Amsterdam.
• The acyclic subgraph problem, Report BW 26/73, Mathematisch Centrum, Amsterdam.
• Bases for Boolean rings (with P. van Emde Boas), Report 73-05, Mathematisch Instituut, Universiteit van Amsterdam.

• Euclid's algorithm in cyclotomic fields, Report 74-01, Mathematisch Instituut, Universiteit van Amsterdam.
• Eindige lichamen, ch. IV in: Algebraïsche vergelijkingen, Vakantiecursus 1974, VC 28/74, Mathematisch Centrum, Amsterdam.
• Rational functions invariant under a finite abelian group, Invent. Math. 25, 299―325.
• Simple abelian varieties having a prescribed formal isogeny type (with F. Oort), J. Pure Appl. Algebra 4, 4–53.
• A sharpened version of the Aanderaa-Rosenberg conjecture (with M.R. Best and P. van Emde Boas), Report 30/74, Mathematisch Centrum, Amsterdam.

• Necessary conditions for the existence of perfect Lee codes, Report ZN 59/75, Mathematisch Centrum, Amsterdam.
• Lectures on Euclidean rings, Fakultät für Mathematik, Universität Bielefeld.
• Abelian extensions of arbitrary fields (with W. Kuyk), Math. Ann. 216, 99–104.
  
• Euclid's algorithm in cyclotomic fields, J. London Math. Soc. 10, 457–465.
• Linear independence of cosecant values (with H. Jager), Nieuw Arch. Wisk. (3) 23, 131–144.
• Arithmetische codes, ch. VIII in: Inleiding in de coderingstheorie, ZC 87/75, Mathematisch Centrum, Amsterdam.

• Euclidean number fields of large degree, Report 76-09, Mathematisch Instituut, Universiteit van Amsterdam.
• K2 of a global field consists of symbols, pp. 69–73 in: M.R. Stein (ed.), Algebraic K-theory, Proceedings of the conference held at Northwestern University, Lecture Notes in Mathematics 551, Springer-Verlag, Heidelberg.
• Arithmetische codes, ch. 10 in: J.H. van Lint (ed.), Inleiding in de coderingstheorie, MC Syllabus 31, Mathematisch Centrum, Amsterdam.

• On Artin's conjecture and Euclid's algorithm in global fields, Report 77-03, Mathematisch Instituut, Universiteit van Amsterdam.
• Euclidean number fields of large degree, Invent. Math. 38, 237–254.
• Euclidische getallenlichamen (Ph.D. thesis), Mathematisch Centrum, Amsterdam.
• On Artin's conjecture and Euclid's algorithm in global fields, Invent. Math. 42, 201– 224.
• On the algebraic closure of two, Proc. Kon. Ned. Akad. Wet. series A 80, 389–396.

• Nim multiplication, I.H. E. S., Bures-sur-Yvette.
• Euclidean ideal classes, I.H. E. S., Bures-sur-Yvette.
• Artin's conjecture on primes with prescribed primitive roots, Sém. Delange-Pisot- Poitou 18 no. 14.
• Perfect arithmetic codes, Sém. Delange-Pisot-Poitou 19 no. 15.
• Quelques exemples d'anneaux euclidiens, C.R. Acad. Sc. Paris Sér. I Math. 286, 683– 685.

• Euclidean number fields 1, Math. Intelligencer 2 (1), 6–15.
• Nim multiplication, Sém. théorie des nombres, Bordeaux, 1977/78, no. 11.
• Euclidean ideal classes, Astérisque 61, 121–131.
• Vanishing sums of roots of unity, pp. 249–268 in: P.C. Baayen, D. van Dulst and J. Oosterhoff (eds), Proceedings bicentennial congress Wiskundig Genootschap, Math. Centre Tracts 100 /101, Mathematisch Centrum, Amsterdam.
• Miller's primality test, Inform. Process. Lett. 8, 86–88.

• Grothendieck groups of abelian group rings, Report 80-04, Mathematisch Instituut, Universiteit van Amsterdam.
• On the calculation of regulators and class numbers of quadratic fields, Report 80-08, Mathematisch Instituut, Universiteit van Amsterdam.
• Primality testing, pp. 41–60 in: Studieweek getaltheorie en computers, Mathematisch Centrum, Amsterdam.
• Rational functions invariant under a cyclic group, pp. 91–99 in: P. Ribenboim (ed.), Proceedings of the Queen's number theory conference, 1979, Queen's papers in pure and applied mathematics 54, Kingston.
• Euclidean number fields 2, Math. Intelligencer 2 (2), 73–77.
• Euclidean number fields 3, Math. Intelligencer 2 (2), 99–103.

• Grothendieck groups of abelian group rings, J. Pure Appl. Algebra 20, 173–193.
• Primality testing algorithms, Séminaire Bourbaki 33 exp. no. 576, pp. 243–257 in Lecture Notes in Mathematics 901, Springer-Verlag, Heidelberg.
• Primality testing with Frobenius symbols, C.-R. des Journées de théorie analytique et élémentaire des nombres, Reims.
• Integer programming with a fixed number of variables, Report 81-03, Mathematisch Instituut, Universiteit van Amsterdam.

• On a question of Colliot-Thélène, pp. 143–147 in: M.-J. Bertin (ed.), Séminaire de théorie des nombres Paris 1980-1981, Progress in Mathematics 22, Birkhäuser, Boston.
• Primaliteit en factorisatie, pp. 69–81 in: P.M.B. Vitányi, J. van Leeuwen and P. van Emde Boas (eds), Colloquium complexiteit en algoritmen, deel 2, MC syllabus 48.2, Mathematisch Centrum, Amsterdam.
• On the calculation of regulators and class numbers of quadratic fields, pp. 123–150 in: J. Armitage (ed.), Journées Arithmétiques 1980, London Math. Soc. Lecture Note Ser. 56, Cambridge University Press, Cambridge.
• Factoring polynomials with rational coefficients (with A.K. Lenstra and L. Lovász), Report 82-06, Mathematisch Instituut, Universiteit van Amsterdam; Report IW 195/82, Mathematisch Centrum, Amsterdam.
• Primality testing with Artin symbols, pp. 341–347 in: N. Koblitz (ed.), Number theory related to Fermat's last theorem, Progress in Mathematics 26, Birkhäuser, Boston.
• Factoring polynomials with rational coefficients (with A.K. Lenstra and L. Lovász), Math. Ann. 261, 515–534.
• Primality testing and Jacobi sums (with H. Cohen), Report 82-18, Mathematisch Instituut, Universiteit van Amsterdam.
• Arithmetic codes, ch. 10 in: J.H. van Lint, Introduction to coding theory, Graduate Texts in Mathematics 86, Springer-Verlag, New York.
• Reduced bases for lattices and factorization of polynomials, Sém. téorie des nombres, Bordeaux, 1981/82, no. 35.

• Computational methods in number theory (edited with R. Tijdeman), Math. Centre Tracts 154/155, Mathematisch Centrum, Amsterdam; second edition, 1984.
• Introduction, pp. 1–6 in 1983a.
• Primality testing, pp. 55–77 in 1983a.
• Primality and factorization, pp. 13–15 in: E.C. van der Meulen (ed.), Proceedings of the fourth symposium on information theory in the Benelux, Leuven.
• Snelle priemgetaltests, Wiskunde en onderwijs 9, 171–178.
• Fast prime number tests, Nieuw Arch. Wisk. (4) 1, 133–144.
• Divisors in residue classes, Report 83-03, Mathematisch Instituut, Universiteit van Amsterdam.
• Abelian varieties having very bad reduction (with F. Oort), Report 315, Mathematisch Instituut, Rijksuniversiteit Utrecht.
• Integer programming with a fixed number of variables, Math. Oper. Res. 8, 538–548.

• Primality testing and Jacobi sums (with H. Cohen), Math. Comp. 42, 297–330.
• Divisors in residue classes, Math. Comp. 42, 331–340.
• A Monte Carlo factoring algorithm with linear storage (with C. P. Schnorr), Math. Comp. 43, 289–311.
• Heuristics on class groups (with H. Cohen), pp. 26–36 in: Number theory, New York 1982, Lecture Notes in Mathematics 1052, Springer-Verlag, Heidelberg.
• Heuristics on class groups of number fields (with H. Cohen), pp. 33–62 in: H. Jager (ed.), Number theory, Noordwijkerhout 1983, Lecture Notes in Mathematics 1068, Springer-Verlag, Heidelberg.
• Integer programming and cryptography, Math. Intelligencer 6 (3), 14–19.
• Galois theory and primality testing, Report 84-30, Mathematisch Instituut, Universiteit van Amsterdam.

• Abelian varieties having purely additive reduction (with F. Oort), J. Pure Appl. Algebra 36, 281–298.
• Galois theory for schemes (lecture notes), Mathematisch Instituut, Universiteit van Amsterdam.
• A normal basis theorem for infinite Galois extensions, Proc. Kon. Ned. Akad. Wet. series A 88, 221–228.
• Galois theory and primality testing, pp. 169–189 in: I. Reiner, K. Roggenkamp (eds), Orders and their applications, Lecture Notes in Mathematics 1142, Springer-Verlag, Heidelberg.
• Tests rapides de nombres premiers, Mathématique et Pédagogie 52, 57–64.

• Finding irreducible polynomials over finite fields (with L.M. Adleman), Proc. 18th Annual ACM Symp. on Theory of Computing (STOC), Berkeley, May 28–30, 350–355.
• Primality testing, pp. 269–287 in: J.W. de Bakker, M. Hazewinkel, J.K. Lenstra (eds), Mathematics and computer science, Proceedings of the CWI symposium, November 1983, CWI Monograph 1, North-Holland, Amsterdam.
• Factoring integers with elliptic curves, Report 86-18, Mathematisch Instituut, Universiteit van Amsterdam.
• Elliptic curves and number-theoretic algorithms, Report 86-19, Mathematisch Instituut, Universiteit van Amsterdam.
• Efficient algorithms in number theory (abstract), International Congress of Mathematicians, Berkeley.
• Codes from algebraic number fields, pp. 95–104 in: M. Hazewinkel, J.K. Lenstra, L.G.L.T. Meertens (eds), Mathematics and computer science II, Fundamental contributions in the Netherlands since 1945, CWI Monograph 4, North-Holland, Amsterdam.
• Euclid's algorithm in large Dedekind domains, Report 86-25, Mathematisch Instituut, Universiteit van Amsterdam.

• Primitive normal bases for finite fields (with R. J. Schoof), Math. Comp. 48, 217–231.
• Algorithms in number theory (with A.K. Lenstra), Technical Report 87-008, Department of Computer Science, The University of Chicago.
• Factoring integers with elliptic curves, Ann. of Math. 126, 649–673.

• Elliptic curves and number-theoretic algorithms, pp. 99–120 in: Proceedings of the International Congress of Mathematicians, Berkeley, 1986, American Mathematical Society, Providence.
• Euclid's algorithm in large Dedekind domains, J. Indian Math. Soc. 50 (1986), 41–47.

• Subgroups close to normal subgroups (with G. Bergman), J. Algebra 127, 80–97.
• Über das Fortsetzen von Bewertungen in vollständigen Körpern (with P. Stevenhagen), Arch. Math. (Basel) 53, 547–552.

• Automorphisms of finite fields, J. Number Theory 34, 33–40.
• Groups with finitely many non-normal subgroups (with N. S. Hekster), Arch. Math. (Basel) 54, 225–231.
• Algorithms for finite fields, pp. 76–85 in: J.H. Loxton (ed.), Number theory and cryptography, London Math. Soc. Lecture Note Ser. 154, Cambridge University Press, Cambridge.
• The number field sieve (extended abstract) (with A.K. Lenstra, M. S. Manasse, and J.M. Pollard), Proc. 22nd Annual ACM Symp. on Theory of Computing (STOC), Baltimore, May 14–16, 564–572.
• Forms in odd degree extensions and self-dual normal bases (with E. Bayer-Fluckiger), Amer. J. Math. 112, 359–373.
• Algorithms in number theory (with A.K. Lenstra), pp. 673–715 in: J. van Leeuwen (ed.), Handbook of theoretical computer science, Vol. A, Algorithms and complexity, Elsevier, Amsterdam and The MIT Press, Cambridge, Massachusetts.
• Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice (with J.C. Lagarias and C. P. Schnorr), Combinatorica 10, 343–358.
• Applied number theory, pp. 5–14 in: Number Theory, Proceedings of a Symposium, May 4, 1989, National Research Council, Washington, D.C.

• Perfect squares don't exist, Math. Intelligencer 13 (1), 40.
• Finding isomorphisms between finite fields, Math. Comp. 56, 329–347.
• Quotients of group rings arising from two-dimensional representations (with N. Boston and K.A. Ribet), C. R. Acad. Sci. Paris Sér. I Math. 312, 323–328.
• Primes of degree one and algebraic cases of Cebotarev's theorem (with P. Stevenhagen), Enseign. Math. (2) 37, 17–30.
• On the Chor-Rivest knapsack cryptosystem, J. Cryptology 3, 149–155.

• Algorithms in algebraic number theory, Bull. Amer. Math. Soc. 26, 211–244.
• The number field sieve (NFS), Sec. 5.1.3, pp. 40–44 in: Th. Beth, M. Frisch, G. J. Simmons (eds), Public-key cryptography: state of the art and future directions, Lecture Notes in Comput. Sci. 578, Springer-Verlag, Berlin.
• A rigorous time bound for factoring integers (with C. Pomerance), J. Amer. Math. Soc. 5, 483–516. 5
• On the inverse Fermat equation, Discrete Math. 106/107, 329–331.
• Optimal normal bases (with Shuhong Gao), Designs, Codes and Cryptography 2, 315– 323.
• Numerieke aspecten van de vergelijking van Cantor, 5 pp., in: P. van Emde Boas et al. (eds), "Is er nog nieuws?" aangeboden aan Prof. Dr Th. J. Dekker, Amsterdam.

• The Tate conjecture for almost ordinary Abelian varieties over finite fields (with Yu.G. Zarhin), pp. 179–194 in: F.Q. Gouvêa, N. Yui (eds), Advances in number theory, The Proceedings of the Third Conference of the Canadian Number Theory Association, 1991, Oxford University Press.
• The development of the number field sieve (edited with A.K. Lenstra), Lecture Notes in Mathematics 1554, Springer-Verlag, Heidelberg.
• The number field sieve: an annotated bibliography, pp. 1–3 in 1993b.
• The number field sieve (with A.K. Lenstra, M. S. Manasse, and J.M. Pollard), pp. 11–42 in 1993b.
• Factoring integers with the number field sieve (with J. P. Buhler and C. Pomerance), pp. 50–94 in 1993b.
• The factorization of the ninth Fermat number (with A.K. Lenstra, M. S. Manasse, and J.M. Pollard), Math. Comp. 61, 319–349; Addendum, ibid. 64 (1995), 1357.
• Continued fractions and linear recurrences (with J.O. Shallit), Math. Comp. 61, 351– 355.
• Generating units modulo an odd integer by addition and subtraction, Acta Arith. 64, 383–388.
• A hyperelliptic smoothness test, I (with J. Pila and C. Pomerance), Philos. Trans. Roy. Soc. London Ser. A 345, 397–408.

• Sharp characters with only one rational value (with D. Alvis, M. Kiyota, and S. Nozawa), Comm. in Algebra 22, 95–115.
• Finite complete intersection algebras (with B. de Smit), Report 9453/B, Econometric Institute, Erasmus University Rotterdam.
• Chebotarëv and his density theorem (with P. Stevenhagen), Report 94-25, Faculteit Wiskunde en Informatica, Universiteit van Amsterdam.

• Approximating rings of integers in number fields (with J.A. Buchmann), Journal de Théorie des Nombres de Bordeaux 6, 221–260.
• Complete intersections and Gorenstein rings, pp. 99–109 in: J. Coates, S.T. Yau (eds), Elliptic curves, modular forms, and Fermat's last theorem, International Press, Boston.
• Complete systems of two addition laws for elliptic curves (with W. Bosma), J. Number Theory 53, 229–240.
• Het ontbinden van grote getallen in priemfactoren, Nieuwe Wiskrant 15, 7–15.
• Does the set of points of an elliptic curve determine the group? (with J. Pila), in: W. Bosma, A. van der Poorten (eds), Computational algebra and number theory, Sydney 1992, Kluwer, Dordrecht, pp. 111–118.
• Rekenen met priemgetallen, Wiskunde en Onderwijs 21, 452–468.
• Computing Jacobi symbols in algebraic number fields, Nieuw Arch. Wisk. 13, 421–426.

• My butter, garçon (with E.W. Howe and D. P. Moulton), p. 28 in: A. van der Poorten, Notes on Fermat's Last Theorem, Wiley, New York; reprinted on p. 306 of: S. Singh, Fermat's last theorem, Fourth Estate, London, 1997.
• Abelian subvarieties (with F. Oort and Yu.G. Zarhin), J. Algebra 180, 513–516.
• Complex multiplication structure of elliptic curves, J. Number Theory 56, 227–241.
• Chebotarëv and his density theorem (with P. Stevenhagen), Math. Intelligencer 18 (2), 26–37.
• Wiskunde en onbegrip, Nieuw Arch. Wisk. 14, 33–43.
• A family of exceptional polynomials in characteristic three (with M. Zieve), pp. 209– 218 in: S.D. Cohen, H.G. Niederreiter (eds), Finite fields and applications, Cambridge University Press, Cambridge.

• Explicit construction of universal deformation rings (with B. de Smit), pp. 313–326 in: G. Cornell, J.H. Silverman, G. Stevens (eds), Modular forms and Fermat's last theorem, Springer, New York.
• Class field theory and the first case of Fermat's last theorem (with P. Stevenhagen), pp. 499–503 in: G. Cornell, J.H. Silverman, G. Stevens (eds), Modular forms and Fermat's last theorem, Springer, New York.
• Finite complete intersection algebras and the completeness radical (with B. de Smit), J. Algebra 196, 520–531.

• Andries en zijn kameraden (edited with Ruud Koning, Jan Karel Lenstra, and Tom Wansbeek), Amsterdam, 26 maart 1998.
• Het wijnmengersprobleem van Diophantus, pp. 36–41 in 1998a.
• Linearly equivalent actions of solvable groups (with B. de Smit), 16 pages, Report W98–19, Mathematical Institute, University of Leiden.

• Finding small degree factors of lacunary polynomials, pp. 267–276 in: K. Gyory, H. Iwaniec, J. Urbanowicz (eds), Number theory in progress, De Gruyter, Berlin.
• On the factorization of lacunary polynomials, pp. 277–291 in: K. Gyory, H. Iwaniec, J. Urbanowicz (eds), Number theory in progress, De Gruyter, Berlin.
• Archimedes, The cattle problem (with S. J. P. Hillion), Mercator Pers, Santpoort.
• Rationale punten op algebraïsche oppervlakken, Nieuw Arch. Wisk. 17, 475–481.

• Artin reciprocity and Mersenne primes (with P. Stevenhagen), Nieuw Arch. Wisk. (5) 1, 44–54.
• Linearly equivalent actions of solvable groups (with B. de Smit), J. Algebra 228, 270– 285.

• Factoring polynomials over special finite fields (with E. Bach and J. von zur Gathen), Finite fields and their applications 7, 5–28.
• Aeternitatem cogita, Nieuw Arch. Wisk. (5) 2, 23–28.
• Aeternitatem cogita, Universiteit Leiden, 20 pp., September 2001.
• Het leukste van wiskunde is een bewijs, Natuur & Techniek 69 (10), 66–72.
• Aeternitatem cogita, Nieuwe Wiskrant 21 (1), 34–41.
• Flags and lattice basis reduction, pp. 37–51 in: C. Casacuberta et al. (eds), European congress of mathematics, Barcelona, July 10-14, 2000, vol. I, Birkhäuser Verlag, Basel.

• Solving the Pell equation, Notices Amer. Math. Soc. 49, 182–192.
• A hyperelliptic smoothness test II (with J. Pila and C. Pomerance), Proc. London Mathematical Soc. (3) 84, 2361–2401.
• On a problem of Garcia, Stichtenoth, and Thomas, Finite fields and their applications 8, 166–170.
• On hats and other covers (with G. Seroussi), ISIT 2002, Lausanne, Switzerland.

• The mathematical structure of Escher's Print Gallery (with B. de Smit), Notices Amer. Math. Soc. 50, 446–451.

• La struttura matematica della Galleria di stampe di Escher (with B. de Smit), pp. 217–226 in: M. Emmer (ed.), Matematica e cultura 2004, Springer-Verlag, Milano.
• Escher en het Droste-effect, pp. 21–30 in: Natuurkundige Voordrachten Nieuwe Reeks 82, Diligentia, 's-Gravenhage.

• Over de fabricage van priemgetallen, Verslag van de gewone vergadering van de Afdeling Natuurkunde, deel 114, nr. 1, 9–13, Koninklijke Nederlandse Akademie van Wetenschappen.
• Profinite Fibonacci numbers, Nieuw Arch. Wisk. (5) 6, 297–300.
• Escher en het droste-effect, pp. 131–144 in: B. Mols (ed.), Het raadsel van informatie, Boom, Amsterdam.

• Profinite Fibonacci numbers, Newsletter of the European Mathematical Society 61 (September 2006), 15–19.

• Commentary on H: Divisibility and congruences, in: Andrzej Schinzel, Selected papers, European Mathematical Society, Zürich, 2007, vol. II, 901–902.
• Detecting perfect powers by factoring into coprimes (with D. J. Bernstein and J. Pila), Math. Comp. 76, 385–388.
• Het hoofd en de boekenkast (3 pages), published in a collection of essays dedicated to Jan Karel Lenstra on the occasion of his sixtieth birthday.

• Solving the Pell equation, pp. 1–23 in: J. P. Buhler, P. Stevenhagen (eds), Algorithmic number theory, Mathematical Sciences Research Institute Publications, Cambridge University Press.
• Lattices, pp. 127–181 in: J. P. Buhler, P. Stevenhagen (eds), Algorithmic number theory, Mathematical Sciences Research Institute Publications, Cambridge University Press.

• Ode aan het getal 43, Nieuw Arch. Wisk. (5) 10, 240–244.

• Irreducible cubics modulo five, Amer. Math. Monthly 117, 817–821.