# Analytic Arithmetic in Algebraic Number Fields (Lecture Notes in Mathematics)

Analytic Arithmetic in Algebraic Number Fields (Lecture Notes in Mathematics)

Spriger; 1 edition (September 26, 1986) | ISBN: 3540167846 | 192 pages | File type: PDF | 2 mb

This book is an improved version of our memoir that appeared in Bonner Mathematische Schriften, [64]. Its purpose is twofold: first, we give a complete relatively self-contained proof of the theorem concerning analytic continuation and natural boundary of Euler products (sketched in Chapter III of [64]) and describe applications of Dirichlet series represented by Euler products under consideration; secondly, we review in detail classical methods of analytic number theory in fields of algebraic numbers. Our presentation of these methods (see Chapter I) has been most influenced by the work of E. Landau, [40], [42], E. Hecke, [24], and A. Weil, [91] (cf. also [87]). In Chapter II we develop formalism of Euler products generated by polynomials whose coefficients lie in the ring of virtual characters of the (absolute) Weil group of a number field and apply it to study scalar products of Artin-Weil Lfunctions.

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