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.
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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. Brudern. 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. Pade approximation for words generated
by certain substitutions, and Hankel determinants; J. Tamura. On Sturmian
Sequences which are invariant under some substitutions; S. Yasutomi.
