**Hindustan Book Agency**

Volume: 63;
2013;
244 pp;
Softcover

MSC: Primary 11;
**Print ISBN: 978-93-80250-53-3
Product Code: HIN/63**

List Price: $52.00

AMS Member Price: $41.60

# Diophantine Approximation and Dirichlet Series

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*Hervé Queffélec; Martine Queffélec*

A publication of Hindustan Book Agency

This self-contained book is intended to be read with profit
by beginners as well as researchers. It is devoted to Diophantine
approximation, the analytic theory of Dirichlet series, and some
connections between these two domains, which often occur through the
Kronecker approximation theorem. Accordingly, the book is divided
into seven chapters, the first three of which present tools from
commutative harmonic analysis, including a sharp form of the
uncertainty principle, ergodic theory and Diophantine approximation to
be used in the sequel. A presentation of continued fraction
expansions, including the mixing property of the Gauss map, is
given.

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.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

#### Readership

Researchers interested in number theory with an emphasis on Diophantine approximation and the anyalytic theory of Dirichlet series.