by Takashi Aoki (Kinki University, Japan) , Shigeru Kanemitsu (Kinki University, Japan) , & Jianya Liu (Shandong University, China)

This volume aims at collecting survey papers which give broad and enlightening perspectives of various aspects of number theory.

Kitaoka's paper is a continuation of his earlier paper published in the last proceedings and pushes the research forward. Browning's paper introduces a new direction of research on analytic number theory — quantitative theory of some surfaces and Bruedern et al's paper details state-of-the-art affairs of additive number theory. There are two papers on modular forms — Kohnen's paper describes generalized modular forms (GMF) which has some applications in conformal field theory, while Liu's paper is very useful for readers who want to have a quick introduction to Maass forms and some analytic-number-theoretic problems related to them. Matsumoto et al's paper gives a very thorough survey on functional relations of root system zeta-functions, Hoshi–Miyake's paper is a continuation of Miyake's long and fruitful research on generic polynomials and gives rise to related Diophantine problems, and Jia's paper surveys some dynamical aspects of a special arithmetic function connected with the distribution of prime numbers. There are two papers of collections of problems by Shparlinski on exponential and character sums and Schinzel on polynomials which will serve as an aid for finding suitable research problems. Yamamura's paper is a complete bibliography on determinant expressions for a certain class number and will be useful to researchers.

Thus the book gives a good-balance of classical and modern aspects in number theory and will be useful to researchers including enthusiastic graduate students.

• Recent Progress on the Quantitative Arithmetic of Del Pezzo Surfaces (T Browning)
• Additive Representation in Thin Sequences, VIII: Diophantine Inequalities in Review (J Bruedern et al.)
• Some Diophantine Problems Arising from the Isomorphism of Generic Polynomials (A Hoshi & K Miyake)
• Recent Progress on Dynamics of a Special Arithmetic Function (C-H Jia)
• A Statistical Relation Between Roots of a Polynomial in Different Local Fields II (Y Kitaoka)
• Generalized Modular Functions and Their Fourier Coefficients (W Kohnen)
• Functional Relations for Zeta-Functions of Root Systems (Y Komori et al.)
• A Quick Introduction to Maass Forms (J Y Liu)
• The Number of Non-Zero Coefficients of a Polynomial — Solved and Unsolved (A Schinzel)
• Open Problems on Exponential and Character Sums (I Shparlinski)
• Bibliography on Determinantal Expressions of Relative Class Numbers of Imaginary Abelian Number Fields (K Yamamura)