Number Theory and Its Applications

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.