Number Theory in Progress

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