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Analytic Methods in Arithmetic Geometry (Paperback)
Loot Price: R3,698
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Analytic Methods in Arithmetic Geometry (Paperback)
Series: Contemporary Mathematics
Expected to ship within 10 - 15 working days
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This volume contains the proceedings of the Arizona Winter School
2016, which was held from March 12-16, 2016, at The University of
Arizona, Tucson, AZ. In the last decade or so, analytic methods
have had great success in answering questions in arithmetic
geometry and number theory. The School provided a unique
opportunity to introduce graduate students to analytic methods in
arithmetic geometry. The book contains four articles. Alina C.
Cojocaru's article introduces sieving techniques to study the group
structure of points of the reduction of an elliptic curve modulo a
rational prime via its division fields. Harald A. Helfgott's
article provides an introduction to the study of growth in groups
of Lie type, with $\mathrm{SL}_2(\mathbb{F}_q)$ and some of its
subgroups as the key examples. The article by Etienne Fouvry,
Emmanuel Kowalski, Philippe Michel, and Will Sawin describes how a
systematic use of the deep methods from $\ell$-adic cohomology
pioneered by Grothendieck and Deligne and further developed by Katz
and Laumon help make progress on various classical questions from
analytic number theory. The last article, by Andrew V. Sutherland,
introduces Sato-Tate groups and explores their relationship with
Galois representations, motivic $L$-functions, and Mumford-Tate
groups.
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