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Explicit Formulas
for Regularized Products and Series
PDF
Sofort lieferbar | Lieferzeit: Sofort lieferbar I
ISBN-13:
9783540490418
Veröffentl:
2006
Einband:
PDF
Seiten:
160
Autor:
Dorian Goldfeld
Serie:
Lecture Notes in Mathematics
eBook Typ:
PDF
eBook Format:
PDF
Kopierschutz:
Adobe DRM [Hard-DRM]
Sprache:
Englisch
Beschreibung:
The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulas can be used to describe the quantitative behavior of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from Gaussian test functions, leading to theta inversion formulas and corresponding new types of zeta functions which are Gaussian transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of applications includes the spectral theory of a broad class of manifolds and also the theory of zeta functions in number theory and representation theory. Here the hyperbolic 3-manifolds are given as a significant example.
The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. These explicit formulas can be used to describe the quantitative behavior of various objects in analytic number theory and spectral theory. The present book deals with other applications arising from Gaussian test functions, leading to theta inversion formulas and corresponding new types of zeta functions which are Gaussian transforms of theta series rather than Mellin transforms, and satisfy additive functional equations. Their wide range of applications includes the spectral theory of a broad class of manifolds and also the theory of zeta functions in number theory and representation theory. Here the hyperbolic 3-manifolds are given as a significant example.