Number Theory in Progress

Proceedings of the International Conference on Number Theory organized by the Stefan Banach International Mathematical Center in Honor of the 60th Birthday of Andrzej Schinzel, Zakopane, Poland, June 30-July 9, 1997.

Table of Contents:
Volume 1 Diophantine problems and polynomials: quelques nouveaux resultats sur les nombres de Pisto et de Salem; irreducibility of polynomials and arithmetic progressions with equal products of terms; Mahler's measure and special values of "L"-functions - some conjectures; on the distribution of solutions of Thue's equation; linear independence and divided derivatives of a Drinfeld module; cubic threefolds with six double points; arithmetique et espaces de modules de revetements; on a polynomial with large number of irreducible factors; fractions continues parametrees et critere de Rabinowitsch; the absolute subspace theorem and linear equations with unknowns from a multiplicative group; on the factorization of polynomials with small Euclidean norm; small Salem numbers; variables separated polynomials, the genus 0 problem and moduli spaces; some polynomial idenities related to the "abc"-conjecture; on the distribution of solutions of decomposable form equations; finding small degree factors of lacunary polynomials; on the factorization of lacunary polynomials; specializations of some hyperelliptic Jacobians; Salem numbers and Pisot numbers from stars; on lacunary formal series and their continued fraction expansion; the ultra-divergent series; une remarque sur l'equation de Catalan; the work of Andrzej Schinzel in number theory; algebraic curves with many rational points over finite fields of characteristic 2; Arf equivalence I; the number of irreducible factors of a polynomial, III; identities with covering systems and Appell polynomials; binary recurring sequences and powers; on Mahler's measure for polynomials in several variables; polynomials that divide many "k"-nomials; solution trees of polynomial congruences modulo prime powers; the equation axn-1=byq with ab>1; transcendence bases of the algebra of vector invariants for a symmetric group; some applications of Schinzel's hypothesis to diophantine equations; on the Milnor exact sequence for rational quadratic forms; some notes on monodromy groups of polynomials; integer valued entire functions on Cartesian products; on a conjecture of Schinzel and Tijdeman. Volume 2 Elementary and analytic number theory: on some convex lattice polytopes; digital blocks in linear numeration systems; on irregularities of distribution in shifts and dilation of integer sequences; addition of integer sequences and subsets of real tori; Kloosterman sums for the modular group; Hecke series values of holomorphic cusp forms in the centre of the critical strip; bounds for frequencies of residues of regular second-order recurrences "modulo pr"; differential inequalities for Iwaniec's "q" functions; when is the product of two Hecke eigenforms an eigenform?; grandes valeurs de la fonction "dk"; on a multiplicative analogue of Goldbach's conjecture; on two conjectures of Sierpioski concerning the arithmetic functions "s" and "f"; residue classes free of values of Euler's funtion; Gauss' congruence from Dirichlet's clas