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Perspectives on the Analytic Theory of L-Functions

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Book cover Visions in Mathematics

Part of the book series: Modern Birkhäuser Classics ((MBC))

Abstract

To the general mathematician L-functions might appear to be an esoteric and special topic in number theory. We hope that the discussion below will convince the reader otherwise. Time and again it has turned out that the crux of a problem lies in the theory of these functions. At some level it is not entirely clear to us why L-functions should enter decisively, though in hindsight one can give reasons. Our plan is to introduce L-functions and describe the central problems connected with them. We give a sample (this is certainly not meant to be a survey) of results towards these conjectures as well as some problems that can be resolved by finessing these conjectures. We also mention briefly some of the successful present-day tools and the role they might play in the big picture.

Supported in part by NSF Grants DMS-98-01642 and DMS-99-70386 as well as by grants to the Institute for Advanced Study from the Ambrose Monell Foundation, the Hansmann Membership and the Veblen Fund.

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Authors and Affiliations

  1. Department of Mathematics, Rutgers University, New Brunswick, NJ, 08903-2101, USA

    H. Iwaniec

  2. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    P. Sarnak

Authors
  1. H. Iwaniec
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  2. P. Sarnak
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, University of Tel Aviv, Tel Aviv, 69978, Israel

    N. Alon

  2. School of Mathematics Institute for Advanced Study, Princeton University, Princeton, NJ, 08540, USA

    J. Bourgain

  3. Collège de France, 3, rue d’Ulm, 75231, Paris cedex 05, France

    A. Connes

  4. Institut des Hautes Études Scientifiques, 35, Route de Chartres, 91440, Bures-sur-Yvette, France

    M. Gromov

  5. Department of Mathematics, University of Tel Aviv, Tel Aviv, 69978, Israel

    V. Milman

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Iwaniec, H., Sarnak, P. (2000). Perspectives on the Analytic Theory of L-Functions. In: Alon, N., Bourgain, J., Connes, A., Gromov, M., Milman, V. (eds) Visions in Mathematics. Modern Birkhäuser Classics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0425-3_6

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