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These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t -motives. This volume is aimed at a wide audience of graduate students, mathematicians, and researchers interested in geometry and arithmetic and their connections.

Progress in Mathematics

Contributors: G. Brenner; F. Breuer; K. Conrad; A. Deitmar; C. Deninger; B. Edixhoven; G. Faltings; U. Hartl; R.

Papers and Preprints

Lagarias; V. Maillot; R. Pink; D.

Roessler; and A. JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser. Singhof M. Lapidus, V. Deitmar Hamb. Number theory and dynamical systems on foliated spaces ArXiv Jber. ArXiv W. Singhof Annals of Global Analysis and Geometry 21 , On the nature of the "explicit formulas" in analytic number theory - a simple example ArXiv S.

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Kanemitsu, C. Jia eds. A note on arithmetical topology and dynamical systems ArXiv S. Vostokov, Y. Zarhin eds. Papers Dedicated to A. Parshin on the Occasion of his Sixtieth Birthday. Baldassarri, N. Naumann Diophantine geometry, vol.


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Werner Vector bundles on p-adic curves and parallel transport ArXiv A. Werner Ann. Werner G. Moonen, R. Schoof eds.

Algebra & Number Theory

Werner Algebraic cycles and motives. Lecture Note Ser. Press A dynamical systems analogue of Lichtenbaum's conjectures on special values of Hasse-Weil zeta functions ArXiv Expansive algebraic actions of discrete residually finite amenable groups and their entropy ArXiv K. Schmidt Ergodic Theory Dynam.

Number Fields and Function Fields – Two Parallel Worlds

Systems 3 , p-adic entropy and a p-adic Fuglede--Kadison determinant ArXiv Algebra, arithmetic, and geometry: in honor of Yu. I, Progr. Werner Algebraic and arithmetic structures of moduli spaces Sapporo , Adv.

Cuntz, M. Laca Math. Regulators, entropy and infinite determinants ArXiv Regulators, —, Contemp. Invariant measures on the circle and functional equations ArXiv Horizontal factorizations of certain Hasse-Weil zeta functions - a remark on a paper by Taniyama ArXiv D. Wegner Rend. Padova , 91— A remark on the structure of torsors under an affine group scheme ArXiv Abh.

Cuntz J.

The Norm of the Weierstrass Section

The e-invariant and the spectrum of the Laplacian for compact nilmanifolds covered by Heisenberg groups. Beilinson's conjectures on special values of L-functions. Seminaire de Theorie des Nombres Paris L-functions and Arithmetic.

Jordan Ellenberg - Geometric analytic number theory [February 06, 2017]

Notes , Jannsen, Kleimann, Serre eds. AMS 55 , Part 1, Press Extensions of mixed motives associated to symmetric powers of elliptic curves and to Hecke characters of imaginary quadratic fields. How to recover an L-series from its values at almost all positive integers.

Some remarks on a formula of Ramanujan. A counterexample to smooth leafwise Hodge decomposition for general foliations and to a type of dynamical trace formulas. Contemporary Mathematics , Algebraic cycles and motives. A dynamical systems analogue of Lichtenbaum's conjectures on special values of Hasse-Weil zeta functions.