## Texts and Readings in Mathematics

Diophantine Approximation and Dirichlet Series (Second Edition)

Hervé Queffélec and Martine Queffélec

Chapters four and five present the general theory of Dirichlet series, with classes of examples connected to continued fractions, the famous Bohr point of view, and then the use of random Dirichlet series to produce non-trivial extremal examples, including sharp forms of the Bohnenblust-Hille theorem. Chapter six deals with Hardy-Dirichlet spaces, which are new and useful Banach spaces of analytic functions in a half-plane. Finally, chapter seven presents the Bagchi-Voronin universality theorems, for the zeta function, and r-tuples of L-functions. The proofs, which mix hilbertian geometry, complex and harmonic analysis, and ergodic theory, are a very good illustration of the material studied earlier. Exercises provided at the end of each chapter will be very useful for the reader.

Chapter eight is a new chapter in this second edition. It is devoted to the study of composition operators Cφ on the Hardy space ℋ2 and their complete characterization by Gordon and Hedenmalm. Several misprints and errors have been corrected in the second edition.

Table of Contents

Texts and Readings in Mathematics 80

2021; 312 pp; Paper cover, 9789386279828, Price: INR 670.00

Texts and Readings in Mathematics 80

2021; 312 pp; Paper cover, 9789386279828, Price: INR 670.00