The present collection of papers contains 14 of 72 papers published separately in three volumes under the title Number theory for the Millennium and presented at the Millennium Conference on Number Theory held at Urbana-Champaign. Thirteen of the papers are devoted to concrete mathematical topics related to the „simple“ or multiple Riemann zeta function (Huxley, Matsumoto), the Riemann hypothesis (Balazard), normal numbers (Harman), arithmetical aspects of the theory of curves (Poonen, Perrin-Riou), Diophantine approximation (Tijdeman), the Pell equation (H.Williams), expansion of a given function into a continued fraction (Lorentzen), Waring’s problem (Vaughan and Wooley), pure and mixed exponential sums (Cochrane and Zheng), authomorphic forms (Winnie Li), or to primes in arithmetical progressions (Hooley). Exceptional in this aspect is the paper ‘G. H. Hardy as I knew him’ by R. A. Rankin. All papers certainly fulfil the editors’ hope that a separate publication can help to stimulate the interest in the presented topics or related areas. All of them give the reader an up-to-date information on the development of basic ideas which paved the road to the described major achievements in the subject so that this collection give an integrated picture on main streams in contemporary number theory. As such, it can be recommended to active number theorists and also to a general mathematical audience.

Reviewer:

spor