Number Theory and Its Applications

The contents of this volume range from expository papers on several aspects of number theory, intended for general readers (Steinhaus property of planar regions; experiments with computers; Diophantine approximation; number field sieve), to a collection of research papers for specialists, which are at prestigious journal level. Thus the book leads the reader in many ways not only to the state of the art of number theory but also to its rich garden.
Audience: Researchers and graduate students interested in recent developments in number theory.

Inhalt

Preface. A problem of Steinhaus concerning the existence of a plane set with a certain property; S.D. Adhikari. Self affine tiling and Pisot numeration system; S. Akiyama. A fundamental but unexploited partition invariant; K. Alladi. On Algebraic independence of certain functions related to the elliptic modular function; M. Amou. Fragments by Ramanujan on Lambert Series; B.C. Berndt. Metric theory of Diophantine approximation in the field of complex numbers; V.I. Bernik, M.M. Dodson. The Davenport-Heilbronn Fourier transform method, and some diophantine inequalities; J. Brüdern. On the probabilistic complexity of numerically checking the binary Goldbach conjecture in certain intervals; J.M. Deshouillers, H. te Riele. On the mean square of Hecke L-functions associated to holomorphic cusp forms; S. Egami. Mean Square of an Error Term Related to a Certain Exponential Sum Involving the Divisor Function; J. Furuya. On zeros of the Lerch zeta-function; R. Garunkstis, A. Laurincikas. Power values of products of consecutive integers and binomial coefficients; K. Gyory. A note on Hilbert modular threefolds; Y. Hamahata. Inverse Galois Problem for Dihedral Groups; K. Hashimoto, K. Miyake. On Ramachandra's method for the mean value problems of various L-functions; Y. Kamiya. On the zeros of certain modular forms; M. Kaneko. A weighted integral approach to the mean square of Dirichlet L-functions; M. Katsurada, K. Matsumoto. The mean value theorem of the Riemann zeta-function in the critical strip for short intervals; I. Kuchi, Y. Tanigawa. On inhomogeneous Diophantine approximation and the NST-algorithm; T. Komatsu. Selberg zeta functions of PGL and PSL over function fields; S. Koyama. A Survey on the Number Field Sieve; K. Nakamula. Non-normal class number one problem and the least prime power-residue; R. Okazaki. Higher dimensional modular equations of degree 7; R. Sasaki. Exponential congruences; A. Schinzel. Padé approximation for words generated by certain substitutions, and Hankel determinants; J. Tamura. On Sturmian Sequences which are invariant under some substitutions; S. Yasutomi.