By Jeffrey Adams (auth.), S. D. Chatterji (eds.)

ISBN-10: 3034890788

ISBN-13: 9783034890786

ISBN-10: 3034898975

ISBN-13: 9783034898973

Since the 1st ICM used to be held in Zürich in 1897, it has turn into the head of mathematical gatherings. It goals at giving an summary of the present nation of alternative branches of arithmetic and its functions in addition to an perception into the therapy of unique difficulties of remarkable value. The court cases of the ICMs have supplied a wealthy chronology of mathematical improvement in all its branches and a distinct documentation of latest learn. They shape an crucial a part of each mathematical library. The complaints of the foreign Congress of Mathematicians 1994, held in Zürich from August third to eleventh, 1994, are released in volumes. quantity I includes an account of the association of the Congress, the record of normal individuals, the stories at the paintings of the Fields Medalists and the Nevanlinna Prize Winner, the plenary one-hour addresses, and the invited addresses offered at part conferences 1 - 6. quantity II includes the invited tackle for part conferences 7 - 19. an entire writer index is integrated in either volumes. '...the content material of those remarkable volumes sheds a undeniable mild at the current kingdom of mathematical sciences and anyone doing examine in arithmetic may still glance rigorously at those lawsuits. For youth starting learn, this can be much more vital, so those are a needs to for any critical arithmetic library. The graphical presentation is, as consistently with Birkhäuser, excellent....' (Revue Roumaine de Mathematiques pures et Appliquées)

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**Extra resources for Proceedings of the International Congress of Mathematicians: August 3–11, 1994 Zürich, Switzerland**

**Sample text**

747 In the first product formula (]" and 7 were both arbitrary complex numbers with a large imaginary part, and in the second they were both fixed to run over imaginary quadratic irrationals. The third product formula is a sort of cross between these, because we allow 7 to be any complex number with a large imaginary part, and make (]" run over a set of representatives of imaginary quadratic irrationals of some fixed discriminant d. For simplicity we will assume d < -4 and d squarefree. 1 of the form q-d + O(q), and h is the class number of the imaginary quadratic field of v'd.

2. Cohomology groups of G-line bundles over spherical varieties Recall the definition of a G-vector bundle E over a G-variety X. It consists in a vector bundle p : E --+ X with a G-action on E, such that p is G-equivariant and that G acts linearly on the fibers of p. Then it is known that the cohomology groups Hi(X, E) are rational G-modules. Assume further that k has characteristic zero; then the groups Hi(X, E) are direct sums of finite-dimensional simple G-modules, with multiplicities. When X is spherical, all multiplicities of the Gmodule HO(X, E) are at most equal to the rank of E.

E. cts, Invent. Math. 120 (1995), 161-213. [EZ] M. Eichler and D. Zagier, The theory of Jacobi forms, Progr. Math. 55, Birkhiiuser, Basel/Boston, 1985. H. B. Zagier, On singular moduli, J. Reine Angew. Math. 355 (1985), 191-220. C. Kac, Infinite dimensional Lie algebras, third edition, Cambridge University Press, London and New York, 1990. ) [Ko] W. Kohnen, Modular forms of half integral weight on ro(4), Math. Ann. 248 (1980) 249-266. Spherical Varieties MICHEL BRION Ecole Normale Superieure, 46 allee d'Italie F-69364 Lyon Cedex 7, France Introduction Consider a connected reductive algebraic group G over an algebraically closed field k, a Borel subgroup B of G, and a closed subgroup H C G.

### Proceedings of the International Congress of Mathematicians: August 3–11, 1994 Zürich, Switzerland by Jeffrey Adams (auth.), S. D. Chatterji (eds.)

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