Number Theory: Proceedings of the Turku Symposium on Number Theory in Memory of Kustaa Inkeri, May 31-June 4, 1999 (de Gruyter Proceedings in Mathematics)

These Proceedings contain 22 refereed research and survey articles based on lectures given at the Turku Symposium on Number Theory in Memory of Kustaa Inkeri, held in Turku, Finland, from May 31 to June 4, 1999. The subject of the symposium was number theory in a broad sense with an emphasis on recent advances and modern methods. The topics covered in this volume include various questions in elementary number theory, new developments in classical Diophantine problems - in particular of the Fermat and Catalan type, the ABC-conjecture, arithmetic algebraic geometry, elliptic curves, Diophantine approximations, Abelian fields, exponential sums, sieve methods, box splines, the Riemann zeta-function and other Dirichlet series, and the spectral theory of automorphic functions with its arithmetical applications. Preface Table of Contents On the life and work of Kustaa Inkeri On the values of certain q-hypergeometric series On the Diophantine equation [xxx] Arithmetical properties of the solutions of certain functional equations Multiple zeta sums via box splines Galois representations attached to elliptic curves and diophantine problems One-sided sifting density hypotheses in Selberg's sieve On characterizations of completely multiplicative arithmetical functions A note on the power residue symbol Exponential sums with a large second derivative Some mean value results for the Riemann zeta-function Direct proofs of some of Euler's results The fourth moment of central values of Hecke series The universality of Dirichlet series attached to finite Abelian groups An irrationality criterion for p-adic binomial series The mean values and the universality of Rankin-Selberg L-functions On the binary additive divisor problem Catalan's equation just before 2000 New analytic problems over imaginary quadratic number fields On number theory and Kustaa Inkeri On Lucas sequence terms of the form kx 2 Stark's question and Popescu's conjecture for abelian L-functions Partial Pell numbers List of participants