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Higher dimensional local fields and \(L\)-functions. (English) Zbl 1008.11060

Fesenko, Ivan (ed.) et al., Invitation to higher local fields. Extended version of talks given at the conference on higher local fields, Münster, Germany, August 29-September 5, 1999. Coventry: Geometry and Topology Publications, Geom. Topol. Monogr. 3, 199-213 (2000).
Summary: This work describes several first steps in extending Tate-Iwasawa’s analytic method to define an \(L\)-function in higher dimensions. For generalizing this method the author advocates the usefulness of the classical Riemann-Hecke approach, his adelic complexes together with his generalization of Krichever’s correspondence. He analyzes dimension 1 types of functions and discusses properties of the lattice of commensurable classes of subspaces in the adelic space associated to a divisor on an algebraic surface.
For the entire collection see [Zbl 0954.00026].

MSC:

11S40 Zeta functions and \(L\)-functions
11R56 Adèle rings and groups
11S80 Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.)
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