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Lectures on N_X(p) (Hardcover)
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Lectures on N_X(p) (Hardcover)
Series: Research Notes in Mathematics
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Lectures on NX(p) deals with the question on how NX(p), the number
of solutions of mod p congruences, varies with p when the family
(X) of polynomial equations is fixed. While such a general question
cannot have a complete answer, it offers a good occasion for
reviewing various techniques in l-adic cohomology and group
representations, presented in a context that is appealing to
specialists in number theory and algebraic geometry. Along with
covering open problems, the text examines the size and congruence
properties of NX(p) and describes the ways in which it is computed,
by closed formulae and/or using efficient computers. The first four
chapters cover the preliminaries and contain almost no proofs.
After an overview of the main theorems on NX(p), the book offers
simple, illustrative examples and discusses the Chebotarev density
theorem, which is essential in studying frobenian functions and
frobenian sets. It also reviews -adic cohomology. The author goes
on to present results on group representations that are often
difficult to find in the literature, such as the technique of
computing Haar measures in a compact -adic group by performing a
similar computation in a real compact Lie group. These results are
then used to discuss the possible relations between two different
families of equations X and Y. The author also describes the
Archimedean properties of NX(p), a topic on which much less is
known than in the -adic case. Following a chapter on the Sato-Tate
conjecture and its concrete aspects, the book concludes with an
account of the prime number theorem and the Chebotarev density
theorem in higher dimensions.
General
Imprint: |
A K Peters Ltd
|
Country of origin: |
United States |
Series: |
Research Notes in Mathematics |
Release date: |
November 2011 |
First published: |
2011 |
Authors: |
Jean-Pierre Serre
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Dimensions: |
229 x 152 x 16mm (L x W x T) |
Format: |
Hardcover
|
Pages: |
174 |
ISBN-13: |
978-1-4665-0192-8 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Number theory >
General
|
LSN: |
1-4665-0192-8 |
Barcode: |
9781466501928 |
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