06728nam 2201429 a 450 991078973090332120210519213339.01-283-37996-197866133799621-4008-4270-010.1515/9781400842704(CKB)2670000000133403(EBL)827807(OCoLC)769343171(SSID)ssj0000575757(PQKBManifestationID)11408626(PQKBTitleCode)TC0000575757(PQKBWorkID)10553428(PQKB)10618809(MiAaPQ)EBC827807(StDuBDS)EDZ0000406946(DE-B1597)447783(OCoLC)979905293(DE-B1597)9781400842704(Au-PeEL)EBL827807(CaPaEBR)ebr10521872(CaONFJC)MIL337996(PPN)199244731(PPN)187959633(EXLCZ)99267000000013340320110826d2012 uy 0engurun#---|u||utxtccrConvolution and equidistribution[electronic resource] Sato-Tate theorems for finite-field Mellin transforms /Nicholas M. KatzCourse BookPrinceton ;Oxford Princeton University Pressc20121 online resource (213 p.)Annals of mathematics studies ;no. 180Description based upon print version of record.0-691-15330-2 0-691-15331-0 Includes bibliographical references and index.Front matter --Contents --Introduction --CHAPTER 1. Overview --CHAPTER 2. Convolution of Perverse Sheaves --CHAPTER 3. Fibre Functors --CHAPTER 4. The Situation over a Finite Field --CHAPTER 5. Frobenius Conjugacy Classes --CHAPTER 6. Group-Theoretic Facts about Ggeom and Garith --CHAPTER 7. The Main Theorem --CHAPTER 8. Isogenies, Connectedness, and Lie-Irreducibility --CHAPTER 9. Autodualities and Signs --CHAPTER 10. A First Construction of Autodual Objects --CHAPTER 11. A Second Construction of Autodual Objects --CHAPTER 12. The Previous Construction in the Nonsplit Case --CHAPTER 13. Results of Goursat-Kolchin-Ribet Type --CHAPTER 14. The Case of SL(2); the Examples of Evans and Rudnick --CHAPTER 15. Further SL(2) Examples, Based on the Legendre Family --CHAPTER 16. Frobenius Tori and Weights; Getting Elements of Garith --CHAPTER 17. GL(n) Examples --CHAPTER 18. Symplectic Examples --CHAPTER 19. Orthogonal Examples, Especially SO(n) Examples --CHAPTER 20. GL(n) x GL(n) x ... x GL(n) Examples --CHAPTER 21. SL(n) Examples, for n an Odd Prime --CHAPTER 22. SL(n) Examples with Slightly Composite n --CHAPTER 23. Other SL(n) Examples --CHAPTER 24. An O(2n) Example --CHAPTER 25. G2 Examples: the Overall Strategy --CHAPTER 26. G2 Examples: Construction in Characteristic Two --CHAPTER 27. G2 Examples: Construction in Odd Characteristic --CHAPTER 28. The Situation over ℤ: Results --CHAPTER 29. The Situation over ℤ: Questions --CHAPTER 30. Appendix: Deligne's Fibre Functor --Bibliography --IndexConvolution 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.Annals of mathematics studies ;no. 180.Mellin transformConvolutions (Mathematics)Sequences (Mathematics)ArtinГchreier reduced polynomial.Emanuel Kowalski.EulerАoincar formula.Frobenius conjugacy class.Frobenius conjugacy.Frobenius tori.GoursatЋolchinВibet theorem.Kloosterman sheaf.Laurent polynomial.Legendre.Mellin transform.Pierre Deligne.Ron Evans.Tannakian category.Tannakian groups.Zeeev Rudnick.algebro-geometric.autodual objects.autoduality.characteristic two.connectedness.dimensional objects.duality.equidistribution.exponential sums.fiber functor.finite field Mellin transform.finite field.finite fields.geometrical irreducibility.group scheme.hypergeometric sheaf.interger monic polynomials.isogenies.lie-irreducibility.lisse.middle convolution.middle extension sheaf.monic polynomial.monodromy groups.noetherian connected scheme.nonsplit form.nontrivial additive character.number theory.odd characteristic.odd prime.orthogonal case.perverse sheaves.polynomials.pure weight.semisimple object.semisimple.sheaves.signs.split form.supermorse.theorem.theorems.Mellin transform.Convolutions (Mathematics)Sequences (Mathematics)515/.723SI 830rvkKatz Nicholas M.1943-59374MiAaPQMiAaPQMiAaPQBOOK9910789730903321Convolution and equidistribution854265UNINA06497nam 2201645z- 450 991055779790332120220111(CKB)5400000000045424(oapen)https://directory.doabooks.org/handle/20.500.12854/76354(oapen)doab76354(EXLCZ)99540000000004542420202201d2021 |y 0engurmn|---annantxtrdacontentcrdamediacrrdacarrierEnvironmental Hydraulics ResearchBasel, SwitzerlandMDPI - Multidisciplinary Digital Publishing Institute20211 online resource (268 p.)3-0365-0808-2 3-0365-0809-0 This book aims to provide research and engineering applications related to water and hydraulic problems. It is comprised of scientific papers in all topics of hydraulics, in particular, on sustainable water management, environmental hydraulics, ecohydraulics, water-energy nexus, and systems protection and efficiency. Safety and innovation issues, interdisciplinary problems, and linkage of theory to experimental and field applications can also be found within. Solutions of water problems in the form of prediction models, flow simulations, engineering systems, monitoring, management strategies covering scientific investigations and/or experimental or field studies of flow behaviour, hydrodynamics, and climate changes effects and adaptation, new design solutions, innovative approaches in the field of environment, hydraulics, techniques, methods, and analyses to address the new challenges in environmental hydraulics are alo presented and explored. This topic is studied both from a technical and environmental point of view, with the objective of protecting and enhancing the quality of the environment. In a cross-disciplinary field of study, this book comprises open channel/river flows and pressurised systems, combining, among others, new technological, social, and environmental hydraulic challenges, working in water-related fields with available information, new concepts and tools, new design solutions, eco-friendly technologies, and the advanced materials necessary to address the increasing challenges of ensuring a sustainable water environment by promoting the adaptation, flexibility, integration, and sustainability of recognised environmental solutions.Technology: general issuesbicsscADVarea contraction ratiobed shear stressCAEScaffa3dcanal poolCFDCFD modelschannel regulationcohesive sedimentsconsolidationDarcy's lawdegradationdelay timedissolved phosphorusdownstream constant water levelE. colieco-designenergy conceptenergy dissipationenergy dissipation rateenergy storageengineering structureenvironmentally-friendly solutionserosionerosion and energy dissipatersfecal indicator bacteriafeedforward controlfish aggregation effectfish protectionfitting coefficientsflocculationfractal modelfree surface flowsfrozen soilFTWgroundwaterhead losshybrid hydro-wind-solar solutionshydraulic conductivityhydraulic efficiencyhydraulic structure design and managementhydraulic structureshydraulics of renewable energy systemshydro-energyhydrodynamic conditionhydrodynamic modelhydrodynamicshydrologic and ecologic challengeshydropower systemshydrostatic pressure machineintakejet fallingLattice Boltzmann methodlifespanmathematical modellingmicro hydropowernew hydraulic conceptsnew power generationopen sourceover-current capabilitypermeable spur dikephysical modelingPoyang Lakepressure fluctuationspressurised flowspulsating pressurepulsating velocitypumped hydro storage (PHS)release characteristicsriver-lake systemrotating circular flumescale model testSCS curve numbersediment depositionsimilarity lawsliding meshsoil freezing curvesoil structurestormwater reusesubmerge ratiosurface disturbancessuspended vegetationsustainable developmentssustainable efficiencySVFtechnical feasibilityThree Gorges Damtime-averaged pressuretime-averaged velocitytoothed internal energy dissipaters (TIED)transient flowvelocity profilevolume compensationvolume of fluidwater flow diversitywater jetwater levelwater systems efficiencywater wellwater well managementwell ageingwell operationTechnology: general issuesRamos Helena Medt1295536Carravetta ArmandoedtMcNabola AonghusedtAdeyeye KemiedtRamos Helena MothCarravetta ArmandoothMcNabola AonghusothAdeyeye KemiothBOOK9910557797903321Environmental Hydraulics Research3031376UNINA