The Lerch zeta-function is the first monograph on this topic, which
is a generalization of the classic Riemann, and Hurwitz
zeta-functions. Although analytic results have been presented
previously in various monographs on zeta-functions, this is the
first book containing both analytic and probability theory of Lerch
zeta-functions.
The book starts with classical analytical theory (Euler
gamma-functions, functional equation, mean square). The majority of
the presented results are new: on approximate functional equations
and its applications and on zero distribution (zero-free regions,
number of nontrivial zeros etc). Special attention is given to
limit theorems in the sense of the weak convergence of probability
measures for the Lerch zeta-function. From limit theorems in the
space of analytic functions the universitality and functional
independence is derived. In this respect the book continues the
research of the first author presented in the monograph Limit
Theorems for the Riemann zeta-function.
This book will be useful to researchers and graduate students
working in analytic and probabilistic number theory, and can also
be used as a textbook for postgraduate students.
General
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