1.1. Number Theory

Papers in journals and proceedings

S.D. ADHIKARI, N. SARADHA, T.N. SHOREY, R. TIJDEMAN, Transcendental infinite sums, Indag. Math. 12 (2001) 1-14.

E. BACH, J. VON ZUR GATHEN, H.W. LENSTRA, Factoring polynomials over special finite fields, Finite fields and their applications 7 (2001) 5-28.

S. CAVALLAR, Strategies in Filtering in the Number Field Sieve, in: Wieb Bosma (ed.), Algorithmic Number Theory - 4th International Symposium, ANTS-IV, Lecture Notes in Computer Science 1838, Springer, Berlin etc., (2000) 209-231.

S. CAVALLAR, B. DODSON, A.K. LENSTRA, W.M. LIOEN, P.L. MONTGOMERY, B. MURPHY, H.J.J. TE RIELE, K. AARDAL, J. GILCHRIST, G. GUILLERM, P. LEYLAND, J. MARCHAND, F. MORAIN, A. MUFFETT, C. PUTNAM, P. ZIMMERMANN, Factorization of a 512-bit RSA Modulus. In: Bart Preneel (ed.), Advances in Cryptology - EUROCRYPT 2000, Lecture Notes in Computer Science 1807, Springer, Berlin etc., (2000) 1 - 18.

J.-M. DESHOUILLERS, H. TE RIELE, On the probabilistic complexity of numerically checking the binary Goldbach conjecture in certain intervals, S. Kanemitsu and K. Gory (eds.), Number Theory and its Applications, Kluwer, (1999) 89-99.

J. H. EVERTSE, Symmetric improvements of Liouville's inequality: A survey. In: Algebraic Number Theory and Diophantine Analysis, Proc. Conf. Graz, 1998, F. Halter-Koch, R.F. Tichy, eds., Walter de Gruyter, (2000) 129-141.

J.H. EVERTSE, On the norm form inequality $\vert F(x)\vert<= m$, Publ. Math. Debrecen 56 (volume dedicated to the 60th birthday of Prof. K. Gory) (2000) 337-374.

J.H. EVERTSE, Symmetric improvements of Liouville's inequality. J. reine angew. Math. 527 (2000) 69-95.

R.P. GROENEWEGEN, An arithmetic analogue of Clifford's Theorem, Journal de Théorie des Nombres de Bordeaux 13 (2001) 143-156.

L. HAJDU, R. TIJDEMAN, Algebraic aspects of discrete tomography, J. reine angew. Math. 534 (2001) 119-128.

L. HAJDU, R. TIJDEMAN, An algorithm for discrete tomography, Linear Algebra and its Applications 339 (2001) 147-169.

A. HEINIS, The $P(n)/n$-function for bi-infinite words, Theor. Computer Sc. 273 (2002) 35-46.

A. HEINIS, R. TIJDEMAN, Characterisation of asymptotically Sturmian sequences, Publ. Math. Debrecen 56 (2000) 415-430.

H.W. LENSTRA, Flags and lattice basis reduction, 37-51 in: C. Casacuberta et al.(eds), European congress of mathematics, Barcelona, July 10-14, 2000, vol. I, Birkhäuser Verlag, Basel, (2001).

H.W. LENSTRA, B. DE SMIT, Linearly equivalent actions of solvable groups, J. Algebra 228 (2000) 270-285.

H.W. LENSTRA, P. STEVENHAGEN, Artin reciprocity and Mersenne primes Nieuw Arch. Wisk. (5) 1 (2000) 44-54.

P. MOREE, Asymptotically exact heuristics for (near) primitive roots, J. Number Theory 83 (2000) 155-181.

P. MOREE, Approximation of singular series and automata, Manuscripta Math. 101 (2000) 385-389.

P. MOREE, P. STEVENHAGEN, A two variable Artin conjecture, J. Number Theory 85 (2000) 291-304.

P. MOREE, P. STEVENHAGEN, Prime divisors of the Lagarias sequence, J. Théor. Nombres Bordeaux 13 (2001) no. 1, 241-251.

A.J. VAN DER POORTEN, H.J.J. TE RIELE, H.C. WILLIAMS, Computer verification of the Ankeny-Artin-Chowla conjecture for all primes less than 100 000 000 000, Mathematics of Computation 70 (2001) 1311-1328.

H. TE RIELE, Computational sieving applied to some classical number-theoretic problems, 1071-1080 in: Kálmán Gory, Henryk Iwaniec, and Jerzy Urbanowicz (eds.), Number Theory in Progress, Proceedings of the International Conference on Number Theory (Zakopane, Poland, June 30-July 9, 1997), Walter de Gruyter, Berlin etc., (1999).

H. TE RIELE, On the size of solutions of the inequality $\phi(ax+b)<\phi(ax)$, Kazimierz Alster, Jerzy Urbanowicz and Hugh C. Williams (eds.), Public-Key Cryptography and Computational Number Theory (Warsaw, Poland, September 11-15, 2000), Walter de Gruyter, Berlin etc., (2001) 249-255.

J. ROSKAM, A quadratic analogue of Artin's conjecture on primitive roots, J. Number Theory 81 (2000) 93-109.

J. ROSKAM, Prime divisors of linear recurrences and Artin's primitive root conjecture for number fields, J. Thˇor. Nombres Bordeaux 13 (2001) no. 1, 303-314.

J.W. SANDER, R. TIJDEMAN, Low complexity functions and convex sets in $Z^k$, Math. Z. 233 (2000) 123-129.

J.W. SANDER, R. TIJDEMAN, The complexity of function lattices, Theor. Computer Sc. 246 (2000) 195-225.

B. DE SMIT, The cyclic subfield integer index, J. Théor. Nombres Bordeaux 12 (2000) 209-218.

B. DE SMIT, Brauer relations for $S$-class numbers, Acta Arithmetica 98 no. 2 (2001) 133-146.

B. DE SMIT, W. BOSMA, Class number relations from a computational point of view J. Symbolic Comput 31 (2001) 97-112.

B. DE SMIT EN B. EDIXHOVEN, Sur un résultat d'Imin Chen, Mathematical Research Letters 7 (2000) 147-154.

P. STEVENHAGEN, Hilbert's 12th problem, complex multiplication and Shimura reciprocity. Class field theory-its centenary and prospect,, Adv. Stud. Pure Math., 30, Math. Soc. Japan, Tokyo, (2001) 161-176.

R.J. STROEKER, N. TZANAKIS, Computing all integer solutions of a general elliptic equation, In: Algorithmic Number Theory (ed. Wieb Bosma), Proceedings of the 4th International Symposium ANTS-IV, Leiden July 2000, Lecture Notes in Computer Science 1838, Springer, (2000) 551-561.

R. TIJDEMAN, Exact covers of balanced sequences and Fraenkel's conjecture. In: Algebraic Number Theory and Diophantine Analysis, Proc. Intern. Conf. Graz Austria, Ed. by F. Halter-Koch & R.F. Tichy, Walter de Gruyter, Berlin etc., (2000) 467-483.

R. TIJDEMAN, Fraenkel's conjecture for six sequences, Discrete Math. 222 (2000) 223-234.

R.W. VAN DER WAALL, On iterated group actions and direct products, J. Algebra 233 (2000) 57-65.

Ph.D. Theses

A.C.P. GEE, Class fields by Shimura reciprocity, University of Amsterdam. (2001).

A. HEINIS, Arithmetics and combinatorics of words of low complexity, Leiden University (2001).

Reports and pre-prints

V. BERTHÉ, R. TIJDEMAN, Balanced properties of multi-dimensional words, Prétirage no. 2000-05, Institut Math. Luminy, Univ. Marseille 2.

R.P. BRENT, P.L. MONTGOMERY, H.J.J. TE RIELE, Factorizations of Cunningham numbers with bases 13 to 99: millennium edition, CWI Report MAS-R0107, (2001).

J.-H. EVERTSE, Points on subvarieties of tori, Report no. MI 2000-05, Leiden University

J.-H. EVERTSE, On resultant inequalities.

J.-H. EVERTSE, R.G. FERRETTI, Diophantine inequalities on projective varieties, Report MI 2001-19, Leiden University.

J.-H. EVERTSE, N. HIRATA-KOHNO, Wirsing systems and resultant inequalities.

J.-H. EVERTSE, P. MOREE, C.L. STEWART, R. TIJDEMAN, Multivariate Diophantine equations with many solutions, Report MI 2001-20, Leiden University.

J.H. EVERTSE, H.P. SCHLICKEWEI, A quantitative version of the Absolute Subspace Theorem.

J.H. EVERTSE, H.P. SCHLICKEWEI, W.M. SCHMIDT, Linear equations in variables which lie in a multiplicative group.

L. HAJDU, R. TIJDEMAN, Algebraic aspects of emission tomography with absorption, (2001) www.math.leidenuniv.nl/ tijdeman.

J. ROSKAM, Artin's primitive root conjecture for quadratic fields, Report MI 2000-22, Leiden University.

N. SARADHA, T.N. SHOREY, R. TIJDEMAN, Some extensions and refinements of a theorem of Sylvester, Report MI 2000-35, Leiden University.

N. SARADHA, R. TIJDEMAN, On the transcendence of infinite sums of values of rational functions, Report MI 2001-24, Leiden University.

R.J. SIMPSON, R. TIJDEMAN, Multi-dimensional versions of a theorem of Fine and Wilf and a formula of Sylvester, Report MI 2001-28, Leiden University.

B. DE SMIT, On arithmetically equivalent fields with distinct p-class groups, Report MI 2000-39, Leiden University.

R.J. STROEKER, N. TZANAKIS, Computing all integer solutions of a genus 1 equation. Econometric Institute Report Series EI 2001-44, EUR, 20 pages.

R. TIJDEMAN, Some applications of diophantine approximation. Report MI 2000-27, Leiden University.

Other publications

L. DE CLERCK, R.W. VAN DER WAALL, Kijk op Kegelsneden, Doeboek 21, Vierkant voor Wiskunde, (2001) 36 pp.

H.W. LENSTRA, Aeternitatem cogita, Leiden University, 20 pp., September 2001. Appeared also in Nieuw Archief voor Wiskunde (5) 2 (2001), 23-28 and in Nieuwe Wiskrant 21 (1) (2001), 34-41.

H.W. LENSTRA, Het leukste van wiskunde is een bewijs, Natuur & Techniek 69 (10) (2001), 66-72.

P. STEVENHAGEN, Rekenen en getaltheorie, inaugural lecture, Leiden, (2001).

R. TIJDEMAN, Algebraïsche aspecten van discrete tomografie, Versl. Afd. Natk. KNAW Amsterdam 109, (2000) 99-103.

R.W. VAN DER WAALL, Getallen en Groepen, in "Een eeuw wiskunde in boeken", Nieuw Archief voor Wiskunde, 5e Serie, 2 (2001) 68-69 .

R.W. VAN DER WAALL, Johan de Witt, ITW-Nieuws 10 (2000) 30.

R.W. VAN DER WAALL, Frobenius group, in: Encycl. Math. Sc. (Kluwer) deel II (supplement 2000), 233-234.