## Moments, Monodromy, and Perversity. (AM-159): |

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 law," and that figuring out which generalized Sato-Tate law applies to a given family amounts essentially to computing a certain complex semisimple (not necessarily connected) algebraic group, the "geometric monodromy group" attached to that family. Up to now, nearly all techniques for determining geometric monodromy groups have relied, at least in part, on local information. In Introduction 1
- Arithmetic Moduli of Elliptic Curves. (AM-108). [Paperback]
- Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180). [Hardcover and Paperback]
- Exponential Sums and Differential Equations. (AM-124). [Paperback]
- Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116). [Paperback]
- Rigid Local Systems. (AM-139). [Paperback]
- Twisted L-Functions and Monodromy. (AM-150). [Paperback]
- Annals of Mathematics Studies
Phillip A. Griffiths, John N. Mather, and Elias M. Stein, Editors
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