Twisted L-Functions and Monodromy. - Brossura

Katz, Nicholas M.

 
9780691091518: Twisted L-Functions and Monodromy.
Brossura
ISBN 10: 069109151X ISBN 13: 9780691091518
Casa editrice: Princeton University Press, 2002

Sinossi

For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions where we do not even know what sort of answers to expect. This book explores two of them: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? Nicholas Katz answers these questions for families of "big" twists of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still in the function field case, equally well to families of big twists of objects of all sorts, not just to elliptic curves. The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves. The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy. Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry.

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Informazioni sull?autore

Nicholas M. Katz is Professor of Mathematics at Princeton University. He is the author of four other books in this series: Arithmetic Moduli of Elliptic Curves (with Barry Mazur); Gauss Sums, Kloosterman Sums, and Monodromy Groups; Exponential Sums and Differential Equations; and Rigid Local Systems.

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Editore
Princeton University Press
Data di pubblicazione
2002
Lingua
Inglese
ISBN 10 
069109151X
ISBN 13 
9780691091518
Rilegatura
Copertina flessibile
Numero di pagine
246
Contatto del produttore
non disponibile
Persona responsabile
non disponibile

Altre edizioni note dello stesso titolo

9780691091501: Twisted L-functions and Monodromy

Edizione in evidenza

ISBN 10:  0691091501 ISBN 13:  9780691091501
Casa editrice: Princeton Univ Pr, 2002
Rilegato