Pseudodifferential methods in number theory / André Unterberger.

4.4 Congruence algebra and analysis4.5 Miscellany; Chapter 5 The role of modular forms; 5.1 Weyl calculus and modular forms; 5.2 Modular spaces of the metaplectic representation; 5.3 Arithmetic and the harmonic oscillator; Chapter 6 Line measures and modular distributions; 6.1 Which is the right Planck constant?; 6.2 The geometry of the delta factor; 6.3 Revisiting modular distributions; 6.4 Towards algebras of modular distributions; Chapter 7 Arithmetic and the Fuchs calculus; 7.1 A symbolic calculus on the half-line: the Fuchs calculus; 7.2 The Fuchs calculus and the involution inv

7.3 The Fuchs calculus and the Weil positivity criterionChapter 8 A possible approach to the Riemann hypothesis ?; 8.1 p-adic pseudodifferential analysis; 8.2 An adelic version of the main hermitian form; 8.3 Analysis of a failure; 8.4 The case of Dirichlet L-functions; Index; Index of notation; Bibliography