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The content of this book is applications of Tauberian theorems to Dirichlet series and some results on Arithmetic Means, upper and lower bounds for L-series, results on Dirichlet series and a remark on Hardy-Ramanujan "Round numbers". This book contains five Chapters with the first on Number Theory preliminaries and Tauberian theorems of different types. Later chapters give applications of Tauberian theorems to various problems.