Lectures on N_X(p)

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 l-adic cohomology.The author goes on to present results on...

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More by Jean-Pierre Serre

More by Jean-Pierre Serre