LEADER 04808nam 2200745 a 450 001 9910461830703321 005 20210519213339.0 010 $a1-283-37996-1 010 $a9786613379962 010 $a1-4008-4270-0 024 7 $a10.1515/9781400842704 035 $a(CKB)2670000000133403 035 $a(EBL)827807 035 $a(OCoLC)769343171 035 $a(SSID)ssj0000575757 035 $a(PQKBManifestationID)11408626 035 $a(PQKBTitleCode)TC0000575757 035 $a(PQKBWorkID)10553428 035 $a(PQKB)10618809 035 $a(MiAaPQ)EBC827807 035 $a(StDuBDS)EDZ0000406946 035 $a(DE-B1597)447783 035 $a(OCoLC)979905293 035 $a(DE-B1597)9781400842704 035 $a(PPN)199244731 035 $a(PPN)187959633 035 $a(Au-PeEL)EBL827807 035 $a(CaPaEBR)ebr10521872 035 $a(CaONFJC)MIL337996 035 $a(EXLCZ)992670000000133403 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) 608 $aElectronic books. 615 0$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 $a9910461830703321 996 $aConvolution and equidistribution$9854265 997 $aUNINA