Number Theory

Abstract

The average behaviour of the number of solutions of a Diophantine equation and an averaging technique, S.D. Adhikari Pisot numbers and greedy algorithm, S. Akiyama upper bounds for the resultant and Diophantine applications, F. Amoroso logarithmic forms and the abc-conjecture, a. Baker local-global principles and linear algebraic groups, E. Bayer-Fluckiger Diophantine approximation and quadratic fields, J. Beck on a problem of P. Turan concerning irreducible polynomials, A. Berczes et al on products of the terms of linear recurrences, B. Brindza et al on the Kronecker-Gyory specialization, B. Brindza, A. Pinter the Euclidean algorithm in cubic number fields, S. Cavallar a problem of Diophantus and Dickson's conjecture, A. Dujella transcendence of Jacobi's theta series and related results, D. Duverney et al some of my new and almost new problems and results in combinatorial number theory, P. Erdos lower bounds for resultants II, J.H. Evertse distribution of binomial coefficients modulo p., Z.M. Franco the distribution of the zeros of the Riemann zeta function and Baker's theorems, A. Fujii computing power integral bases in algebraic number fields, I. Gaal recent bounds for the solutions of decomposable form equations, K. Gyory on a generalization of the Maillet determinant, S. Kanemitsu, T. Kuzumaki an approximation problem concerning linear recurrences, P. Kiss new methods in algebraic independence, M. Laurent on the arithmetic of simplest sextic fields and related Thue equations, G. Lettl et al algebraic constructions of lattices isodual lattices, J. Martinet real roots of Fibonacci-like polynomials, F. Matyas on some modular identities, G. Melfi complete resolution of some families of Diophantine equations, M. Mignotte experiments on a problem of D. Shanks concerning quadratic fields, T. Nakahara squares in binary recurrence sequences, K. Nakamula, A. Petho algebraic curves over finite fields with many rational points, H. Niederreiter, C. Xing Klein polyhedra for complete decomposable forms, V.I. Parusnikov arithmetical progression formed by Lucas pseudoprimes, A. Rotkiewicz reducibility of polynomials over Kroneckerian fields, A. Schinzel a note on certain exponential Diophantine equations, N. Terai the fundamental lemma of Kubilius and the model of Kubilius in number fields, J.M. Thuswaldner Diophantine properties of digital expansions - R. Tijdenan - exponential Diophantine equations 1986-1996, R.F. Tichy basic algorithms for elliptic curves, H.G. Zimmer. (Part contents).