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100   $a20110826d2012      uy             0
101 0 $aeng
135   $aurun#---|u||u
181   $ctxt
182   $cc
183   $acr
200 10$aConvolution and equidistribution$b[electronic resource] $eSato-Tate theorems for finite-field Mellin transforms /$fNicholas M. Katz
205   $aCourse Book
210   $aPrinceton ;$aOxford $cPrinceton University Press$dc2012
215   $a1 online resource (213 p.)
225 1 $aAnnals of mathematics studies ;$vno. 180
300   $aDescription based upon print version of record.
311 0 $a0-691-15330-2 
311 0 $a0-691-15331-0 
320   $aIncludes bibliographical references and index.
327   $tFront matter --$tContents --$tIntroduction --$tCHAPTER 1. Overview --$tCHAPTER 2. Convolution of Perverse Sheaves --$tCHAPTER 3. Fibre Functors --$tCHAPTER 4. The Situation over a Finite Field --$tCHAPTER 5. Frobenius Conjugacy Classes --$tCHAPTER 6. Group-Theoretic Facts about Ggeom and Garith --$tCHAPTER 7. The Main Theorem --$tCHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility --$tCHAPTER 9. Autodualities and Signs --$tCHAPTER 10. A First Construction of Autodual Objects --$tCHAPTER 11. A Second Construction of Autodual Objects --$tCHAPTER 12. The Previous Construction in the Nonsplit Case --$tCHAPTER 13. Results of Goursat-Kolchin-Ribet Type --$tCHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick --$tCHAPTER 15. Further SL(2) Examples, Based on the Legendre Family --$tCHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith --$tCHAPTER 17. GL(n) Examples --$tCHAPTER 18. Symplectic Examples --$tCHAPTER 19. Orthogonal Examples, Especially SO(n) Examples --$tCHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples --$tCHAPTER 21. SL(n) Examples, for n an Odd Prime --$tCHAPTER 22. SL(n) Examples with Slightly Composite n --$tCHAPTER 23. Other SL(n) Examples --$tCHAPTER 24. An O(2n) Example --$tCHAPTER 25. G2 Examples: the Overall Strategy --$tCHAPTER 26. G2 Examples: Construction in Characteristic Two --$tCHAPTER 27. G2 Examples: Construction in Odd Characteristic --$tCHAPTER 28. The Situation over ?: Results --$tCHAPTER 29. The Situation over ?: Questions --$tCHAPTER 30. Appendix: Deligne's Fibre Functor --$tBibliography --$tIndex
330   $aConvolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods. By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject.
410  0$aAnnals of mathematics studies ;$vno. 180.
606   $aMellin transform
606   $aConvolutions (Mathematics)
606   $aSequences (Mathematics)
610   $aArtin?chreier reduced polynomial.
610   $aEmanuel Kowalski.
610   $aEuler?oincar formula.
610   $aFrobenius conjugacy class.
610   $aFrobenius conjugacy.
610   $aFrobenius tori.
610   $aGoursat?olchin?ibet theorem.
610   $aKloosterman sheaf.
610   $aLaurent polynomial.
610   $aLegendre.
610   $aMellin transform.
610   $aPierre Deligne.
610   $aRon Evans.
610   $aTannakian category.
610   $aTannakian groups.
610   $aZeeev Rudnick.
610   $aalgebro-geometric.
610   $aautodual objects.
610   $aautoduality.
610   $acharacteristic two.
610   $aconnectedness.
610   $adimensional objects.
610   $aduality.
610   $aequidistribution.
610   $aexponential sums.
610   $afiber functor.
610   $afinite field Mellin transform.
610   $afinite field.
610   $afinite fields.
610   $ageometrical irreducibility.
610   $agroup scheme.
610   $ahypergeometric sheaf.
610   $ainterger monic polynomials.
610   $aisogenies.
610   $alie-irreducibility.
610   $alisse.
610   $amiddle convolution.
610   $amiddle extension sheaf.
610   $amonic polynomial.
610   $amonodromy groups.
610   $anoetherian connected scheme.
610   $anonsplit form.
610   $anontrivial additive character.
610   $anumber theory.
610   $aodd characteristic.
610   $aodd prime.
610   $aorthogonal case.
610   $aperverse sheaves.
610   $apolynomials.
610   $apure weight.
610   $asemisimple object.
610   $asemisimple.
610   $asheaves.
610   $asigns.
610   $asplit form.
610   $asupermorse.
610   $atheorem.
610   $atheorems.
615  0$aMellin transform.
615  0$aConvolutions (Mathematics)
615  0$aSequences (Mathematics)
676   $a515/.723
686   $aSI 830$2rvk
700   $aKatz$b Nicholas M.$f1943-$059374
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910789730903321
996   $aConvolution and equidistribution$9854265
997   $aUNINA