Number Theory: Tradition and Modernization

Preface About the book and the conference List of participants Positive finiteness of number systems (S. Akiyama) On a distribution property of the resudual order of a (mod p) -IV (K. Chinen and L. Murata) Diagonalizing 'bad" Hecke operators on spaces of cusp forms (Y.-J. Choie and W. Kohnen) On the Hilbert-Kamke and the Vinogradov problems in additive number theory (V. N. Chubarikov) The Goldbach-Vinogradov theorem in arithmetic progressions (Z. Cui) Densities of sets of primes related to decimal expansion of rational numbers (T. Hadano, Y. Kitaoka, T. Kubota and M. Nozaki) Spherical functions on p-adic homogeneous spaces (Y. Hironaka) On modular forms of weight (6n + 1)=5 satisfying a certain differential equation (M. Kaneko) Some aspects of the modular relation (S. Kanemitsu, Y. Tanigawa, H. Tsukada and M. Yoshimoto) Zeros of automorphic L-functions and noncyclic base change (J. Liu and Y. Ye) Analytic properties of multiple zeta-functions in several variables (K. Matsumoto) Cubic fields and Mordell curves (K. Miyake) Towards the reciprocity of quartic theta-Weyl sums, and beyond (Y.-N. Nakai) Explicit congruences for Euler polynomials (Z.-W. Sun) Square-free integers as sums of two squares (W. Zhai) Some applications of L-functions to the mean value of the Dedekind sums and Cochrane sums (W. Zhang) Index