LIBROS DEL AUTOR: nicholas mkatz

7 resultados para LIBROS DEL AUTOR: nicholas mkatz

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  • Convolution and Equidistribution
    Nicholas M. Katz / Nicholas MKatz
    Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multip...
    Disponible

    137,31 €

  • Moments, Monodromy, and Perversity
    Nicholas M. Katz / Nicholas MKatz
    It is now some thirty years since Deligne first proved his general equidistribution theorem, thus establishing the fundamental result governing the statistical properties of suitably 'pure' algebro-geometric families of character sums over finite fields (and of their associated L-functions). Roughly speaking, Deligne showed that any such family obeys a 'generalized Sato-Tate la...
    Disponible

    183,68 €

  • Twisted L-Functions and Monodromy
    Nicholas M. Katz / Nicholas MKatz
    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 th...
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    137,16 €

  • Rigid Local Systems
    Nicholas M. Katz / Nicholas MKatz
    Riemann introduced the concept of a 'local system' on P1-{a finite set of points} nearly 140 years ago. His idea was to study nth order linear differential equations by studying the rank n local systems (of local holomorphic solutions) to which they gave rise. His first application was to study the classical Gauss hypergeometric function, which he did by studying rank-two local...
    Disponible

    137,22 €

  • Exponential Sums and Differential Equations
    Nicholas M. Katz / Nicholas MKatz
    This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representa...
    Disponible

    157,32 €

  • Gauss Sums, Kloosterman Sums, and Monodromy Groups
    Nicholas M. Katz / Nicholas MKatz
    The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne’s work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constru...
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    123,33 €

  • Arithmetic Moduli of Elliptic Curves
    Barry Mazur / Nicholas M. Katz / Nicholas MKatz
    This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi’s 'Fundamenta Nova' in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapoport. In the past decade mathematicians have made further substantial progress in the field. Th...
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    180,46 €