Pseudodifferential Methods in Number Theory

Resource Information

The work Pseudodifferential Methods in Number Theory represents a distinct intellectual or artistic creation found in Bowdoin College Library. This resource is a combination of several types including: Work, Language Material, Books.

Label

Pseudodifferential Methods in Number Theory

Statement of responsibility

by André Unterberger

Creator

• Unterberger, André

Contributor

• SpringerLink (Online service)

Subject

• Mathematics
• Number theory
• Differential equations, Partial

Language

eng

Summary

Classically developed as a tool for partial differential equations, the analysis of operators known as pseudodifferential analysis is here regarded as a possible help in questions of arithmetic. The operators which make up the main subject of the book can be characterized in terms of congruence arithmetic. They enjoy a Eulerian structure, and are applied to the search for new conditions equivalent to the Riemann hypothesis. These consist in the validity of certain parameter-dependent estimates for a class of Hermitian forms of finite rank. The Littlewood criterion, involving sums of Möbius coeffcients, and the Weil so-called explicit formula, which leads to his positivity criterion, fit within this scheme, using in the first case Weyl's pseudodifferential calculus, in the second case Fuchs'. The book should be of interest to people looking for new possible approaches to the Riemann hypothesis, also to new perspectives on pseudodifferential analysis and on the way it combines with modular form theory. Analysts will have no diffculty with the arithmetic aspects, with which, save for very few exceptions, no previous acquaintance is necessary

Member of

• Pseudo-Differential Operators, Theory and Applications,, 13

Is part of

• Springer eBooks

Literary form

non fiction

Nature of contents

dictionaries

Series statement

Pseudo-Differential Operators, Theory and Applications,

Series volume

13