LEADER 04964nam 2200817 a 450 001 9910968930703321 005 20210519213339.0 010 $a9786613379962 010 $a9781283379960 010 $a1283379961 010 $a9781400842704 010 $a1400842700 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(StDuBDS)EDZ0000406946 035 $a(DE-B1597)447783 035 $a(OCoLC)979905293 035 $a(DE-B1597)9781400842704 035 $a(Au-PeEL)EBL827807 035 $a(CaPaEBR)ebr10521872 035 $a(CaONFJC)MIL337996 035 $z(PPN)199244731 035 $a(PPN)187959633 035 $a(Perlego)735531 035 $a(FR-PaCSA)88838048 035 $a(MiAaPQ)EBC827807 035 $a(FRCYB88838048)88838048 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 $eSato-Tate theorems for finite-field Mellin transforms /$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 $aDescription based upon print version of record. 311 08$a9780691153308 311 08$a0691153302 311 08$a9780691153315 311 08$a0691153310 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 $aSequences (Mathematics) 615 0$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 $a9910968930703321 996 $aConvolution and equidistribution$9854265 997 $aUNINA LEADER 02649nam 2200649 a 450 001 9910962450503321 005 20251012110034.0 010 $a1-283-35491-8 010 $a9786613354914 010 $a0-08-096913-5 035 $a(CKB)2670000000132125 035 $a(EBL)827639 035 $a(OCoLC)769343140 035 $a(SSID)ssj0000630416 035 $a(PQKBManifestationID)11378524 035 $a(PQKBTitleCode)TC0000630416 035 $a(PQKBWorkID)10746131 035 $a(PQKB)11283365 035 $a(MiAaPQ)EBC827639 035 $a(Au-PeEL)EBL827639 035 $a(CaPaEBR)ebr10518418 035 $a(CaONFJC)MIL335491 035 $a(PPN)158613627 035 $a(FR-PaCSA)88973089 035 $a(FRCYB88973089)88973089 035 $a(EXLCZ)992670000000132125 100 $a20111221d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTransmission and distribution electrical engineering /$fC.R. Bayliss and B.J. Hardy 205 $a4th ed. 210 $aOxford $cElsevier$d2012 215 $a1 online resource (1180 pages) 300 $aDescription based upon print version of record. 311 08$a0-08-096912-7 320 $aIncludes bibliographical references and index. 327 $aFront Cover; Transmission and Distribution Electrical Engineering; Copyright Page; Contents; About the Authors; List of Contributors; Preface; Foreword; Index 330 $aThis market leading classic is a true comprehensive on-the-job reference, covering all aspects of getting electricity from the source to user via the power grid. Electric power transmission and distribution is a huge sector, and engineers require the real world guidance of this book in order to upgrade networks to handle smart and renewable sources of power. This new edition covers renewable and distributed energy developments, international regulatory compliance issues with coverage of IEC standards, and new key conversions to US based standards and terminologies Utilising examples 606 $aElectric power transmission 606 $aElectric power distribution 615 0$aElectric power transmission. 615 0$aElectric power distribution. 676 $a621.319 676 $a621.31912 676 $a621.319 700 $aBayliss$b C. R$0786431 701 $aHardy$b B. J$01851256 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910962450503321 996 $aTransmission and distribution electrical engineering$94444949 997 $aUNINA