Isaac Newton Institute for Mathematical Sciences

L-Functions and Arithmetic

1 January - 30 June 1993

Organisers: B. Birch (Oxford), D. Blasius (UCLA), S. Bloch (Chicago), J. Coates (Cambridge), J.-M. Fontaine (Orsay), R. Heath-Brown (Oxford), K. Kato (Tokyo)

Programme theme

Over the last thirty years, number theorists have come to realise that the mysterious connexions between arithmetic problems and the properties of zeta and L-functions, initially discovered in the first half of the nineteenth century, are far more extensive than had been imagined earlier. A vast web of overlapping conjectures has now been formulated, stretching from the Riemann hypothesis and Fermat's last theorem to the Tamagawa numbers of motives. The programme will bring together mathematicians from arithmetical algebraic geometry, automorphic forms, and classical analytic number theory, to work on several of these conjectures.


There will be a regular seminar programme throughout the period, held at 16.15 on Tuesdays and 11.15 on Thursdays. In addition the following periods of concentration have been planned:

All are welcome to attend any of these activities.


The following have accepted invitations to participate in the programme for the periods indicated:

A. Agboola (MSRI), 1 Feb-1 Mar; M. Kurihara (Tokyo), 1 May-30 Jun; P. Berthelot (Rennes), 1 Jun-30 Jun; J-P. Labesse (Paris), 14 Feb-28 Feb; B. Birch (Oxford), 1 Jan-30 Jun; G. Laumon (Orsay), 1 Apr-15 Apr; D. Blasius (UCLA), 1 Apr-30 Jun; B. Mazur (Harvard), 1 May-30 Jun; S. Bloch (Chicago), 1 Apr-30 Jun; W. Messing (Minnesota), 1 May-30 Jun; E. Bombieri (IAS, Princeton), 1 Jun-30 Jun; J. Neukirch (Regensburg), 1 Apr-15 Apr; N. Boston (Illinois), 1 Jan-30 Jun; B. Perrin-Riou (Paris), 1 Jun-30 Jun; C. Bushnell (KCL, London), 1 Apr-30 Apr; M. Ram Murty (McGill), 15 Mar-15 Apr; J. Coates (Cambridge), 1 Jan-30 Jun; D. Ramakrishnan (Caltech), 21 Mar-15 Apr; L. Clozel (Orsay), 1 Apr-30 Apr; M. Rapoport (Wuppertal), 15 Mar-20 Apr; P. Colmez(ENS, Paris), 1 May-31 May; K. Ribet (Berkeley), 12 May-30 Jun; C. Deninger (M), 15 Feb-14 Mar; K. Rubin (Ohio), 30 May-26 Jun; U. de Shalit (Jerusalem), 1 Jun-30 Jun; J-M. Fontaine (Orsay), 1 May-30 Jun; C. Schmidt (Karlsruhe), 15 Mar-18 Apr; A. Granville (Georgia), 1 Jan-30 Jun; P. Schneider (Cologne), 15 Feb-15 Apr; R. Greenberg (Seattle), 1 May-30 Jun; A. Scholl (Durham), 1 Feb-30 Apr; G. Harder (Bonn), 20 Mar-10 Apr; J. Tate (Austin), 1 Jun-30 Jun; M. Harris (Brandeis), 1 Apr-30 Apr; M. Taylor (UMIST), 15 Feb-28 Feb; R. Heath-Brown (Oxford), 1 Apr-15 Jun, 20 Mar-30 Apr; G. Henniart (Orsay), 1 Apr-30 Apr; R. Taylor (Cambridge), 1 Jan-30 Jun; H. Hida (UCLA), 1 Apr-15 May; R. Vaughan (IC, London), 1 Feb-30 Apr; Y. Ihara (Kyoto); 1 Jun-30 Jun; A. Wiles (Princeton), 15 May-30 Jun; L. Illusie (Orsay), 1 Jun-30 Jun; K. Wingberg (Heidelberg), 1 Feb-8 Apr; U. Jannsen (Cologne), 15 Feb-14 Apr; T. Wooley (Ann Arbor), 1 Mar-30 Apr; K. Kato (Tokyo), 15 Mar-15 Jun; N. Yui (Queen's), 1 Jan-31 Mar; V. Kolyvagin (Moscow), 1 May-30 Jun; S. Zhang (Beijing), 1 Jan-31 Mar; S. Kudla (Maryland), 1 Apr-30 Apr.

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