LEADER 06674nam  22017655  450 
001 9910154744703321
005 20230808192420.0
010   $a1-4008-8243-5
024 7 $a10.1515/9781400882434
035   $a(CKB)3710000000631344
035   $a(SSID)ssj0001651276
035   $a(PQKBManifestationID)16425629
035   $a(PQKBTitleCode)TC0001651276
035   $a(PQKBWorkID)14512364
035   $a(PQKB)10492814
035   $a(MiAaPQ)EBC4738723
035   $a(DE-B1597)467977
035   $a(OCoLC)979633762
035   $a(DE-B1597)9781400882434
035   $a(EXLCZ)993710000000631344
100   $a20190708d2016      fg              
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aExponential Sums and Differential Equations. (AM-124), Volume 124 /$fNicholas M. Katz
210  1$aPrinceton, NJ : $cPrinceton University Press, $d[2016]
210  4$dİ1991
215   $a1 online resource (445 pages) $cillustrations
225 0 $aAnnals of Mathematics Studies ;$v305
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a0-691-08599-4 
311   $a0-691-08598-6 
320   $aIncludes bibliographical references.
327   $tFrontmatter -- $tContents -- $tIntroduction -- $tCHAPTER 1. Results from Representation Theory -- $tCHAPTER 2. D.E.'s and D-modules -- $tCHAPTER 3. The Generalized Hypergeometric Equation -- $tCHAPTER 4. Detailed Analysis of the Exceptional Cases -- $tCHAPTER 5. Convolution of D-modules -- $tCHAPTER 6. Fourier Transforms of Kummer Pullbacks of Hypergeometrics -- $tCHAPTER 7. The ?- adic Theory -- $tCHAPTER 8. ?-adic Hypergeometrics -- $tCHAPTER 9. G2 Examples, Fourier Transforms, and Hypergeometrics -- $tCHAPTER 10. ? -adic Exceptional Cases -- $tCHAPTER 11. Reductive Tannakian Categories -- $tCHAPTER 12. Fourier Universality -- $tCHAPTER 13. Stratifications and Convolution -- $tCHAPTER 14. The Fundamental Comparison Theorems -- $tReferences
330   $aThis book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable "coincidences" found "by hand" in the hypergeometric case.
410  0$aAnnals of mathematics studies ;$vno. 124.
606   $aExponential sums
606   $aDifferential equations
610   $aAdjoint representation.
610   $aAlgebraic geometry.
610   $aAlgebraic integer.
610   $aAlgebraically closed field.
610   $aAutomorphism.
610   $aBase change.
610   $aBernard Dwork.
610   $aBig O notation.
610   $aBijection.
610   $aCalculation.
610   $aCharacteristic polynomial.
610   $aCodimension.
610   $aCoefficient.
610   $aCohomology.
610   $aComparison theorem.
610   $aComplex manifold.
610   $aConjugacy class.
610   $aConnected component (graph theory).
610   $aConvolution.
610   $aDeterminant.
610   $aDiagram (category theory).
610   $aDifferential Galois theory.
610   $aDifferential equation.
610   $aDimension (vector space).
610   $aDimension.
610   $aDirect sum.
610   $aDivisor.
610   $aEigenvalues and eigenvectors.
610   $aEndomorphism.
610   $aEquation.
610   $aEuler characteristic.
610   $aExistential quantification.
610   $aExponential sum.
610   $aFiber bundle.
610   $aField of fractions.
610   $aFinite field.
610   $aFormal power series.
610   $aFourier transform.
610   $aFundamental group.
610   $aFundamental representation.
610   $aGalois extension.
610   $aGalois group.
610   $aGauss sum.
610   $aGeneric point.
610   $aGroup theory.
610   $aHomomorphism.
610   $aHypergeometric function.
610   $aIdentity component.
610   $aIdentity element.
610   $aInteger.
610   $aIrreducibility (mathematics).
610   $aIrreducible representation.
610   $aIsogeny.
610   $aIsomorphism class.
610   $aL-function.
610   $aLaurent polynomial.
610   $aLie algebra.
610   $aLogarithm.
610   $aMathematical induction.
610   $aMatrix coefficient.
610   $aMaximal compact subgroup.
610   $aMaximal torus.
610   $aMellin transform.
610   $aMonic polynomial.
610   $aMonodromy theorem.
610   $aMonodromy.
610   $aMonomial.
610   $aNatural number.
610   $aNormal subgroup.
610   $aP-adic number.
610   $aPermutation.
610   $aPolynomial.
610   $aPrime number.
610   $aPullback.
610   $aQuotient group.
610   $aReductive group.
610   $aRegular singular point.
610   $aRepresentation theory.
610   $aRing homomorphism.
610   $aRoot of unity.
610   $aScientific notation.
610   $aSet (mathematics).
610   $aSheaf (mathematics).
610   $aSpecial case.
610   $aSubcategory.
610   $aSubgroup.
610   $aSubring.
610   $aSubset.
610   $aSummation.
610   $aSurjective function.
610   $aSymmetric group.
610   $aTensor product.
610   $aTheorem.
610   $aTheory.
610   $aThree-dimensional space (mathematics).
610   $aTorsor (algebraic geometry).
610   $aTrichotomy (mathematics).
610   $aUnitarian trick.
610   $aUnitary group.
610   $aVariable (mathematics).
615  0$aExponential sums.
615  0$aDifferential equations.
676   $a512/.73
700   $aKatz$b Nicholas M., $059374
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154744703321
996   $aExponential Sums and Differential Equations. (AM-124), Volume 124$92839523
997   $aUNINA