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Titlebook: Automorphic Forms; Anton Deitmar Textbook 2012 Springer-Verlag London 2012 Tate‘s thesis.automorphic L-functions.modular forms.tensor prod

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期刊全称Automorphic Forms
影响因子2023Anton Deitmar
视频video
发行地址Presents an elementary introduction that requires only few pre-requisites.Introduces a host of different techniques such as representation theory, adeles and ideles, and the methods of Tate‘s thesis.C
学科分类Universitext
图书封面Titlebook: Automorphic Forms;  Anton Deitmar Textbook 2012 Springer-Verlag London 2012 Tate‘s thesis.automorphic L-functions.modular forms.tensor prod
影响因子Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles‘s proof of Fermat‘s Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the ‘base field‘ of rational numbers.Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.
Pindex Textbook 2012
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978-1-4471-4434-2Springer-Verlag London 2012
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https://doi.org/10.1007/978-3-642-94529-8sis it is shown that the sum of residues and the sum of orders of poles and zeroes vanishes. The Weierstrass ℘-function is introduced which together with its derivative generates the field doubly periodic functions for given periods. Its Laurent expansion features the first “modular” functions: the
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Zum Begriff einer Genealogie der Schrift all completions of ℚ. In this chapter we discuss the notion of absolute values on fields and their completions. We give several useful descriptions of the field ℚ. of .-adic numbers and compute the additive and multiplicative Haar-measures, which are the equivalents of the Lebesgue measure in the c
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Chicagoer Schule der Soziologie interpret a modular form as a vector in a representation space of the adelic GL(2). We then need to show that any irreducible representation of the adelic GL(2) is a tensor product of local irreducible representations, which is known as the Tensor Product Theorem and generalizes the diagonalization
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