LEADER 04044nam 22009855 450 001 9910154753503321 005 20190708092533.0 010 $a1-4008-8170-6 024 7 $a10.1515/9781400881703 035 $a(CKB)3710000000620071 035 $a(SSID)ssj0001651296 035 $a(PQKBManifestationID)16426393 035 $a(PQKBTitleCode)TC0001651296 035 $a(PQKBWorkID)14003656 035 $a(PQKB)10471831 035 $a(MiAaPQ)EBC4738558 035 $a(DE-B1597)467952 035 $a(OCoLC)979579082 035 $a(DE-B1597)9781400881703 035 $a(EXLCZ)993710000000620071 100 $a20190708d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aLectures on P-Adic L-Functions. (AM-74), Volume 74 /$fKinkichi Iwasawa 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2016] 210 4$d©1972 215 $a1 online resource (116 pages) 225 0 $aAnnals of Mathematics Studies ;$v271 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a0-691-08112-3 320 $aIncludes bibliographical references. 327 $tFrontmatter -- $tPREFACE / $rIwasawa, Kenkichi -- $tCONTENTS -- $t§1. DIRICHLET'S L-FUNCTIONS -- $t§2. GENERALIZED BERNOULLI NUMBERS -- $t§3. p-ADIC L-FUNCTIONS -- $t§4. p-ADIC LOGARITHMS AND p-ADIC REGULATORS -- $t§5. CALCULATION OF Lp (1; ?) -- $t§6. AN ALTERNATE METHOD -- $t§7. SOME APPLICATIONS -- $tAPPENDIX -- $tBIBLIOGRAPHY 330 $aAn especially timely work, the book is an introduction to the theory of p-adic L-functions originated by Kubota and Leopoldt in 1964 as p-adic analogues of the classical L-functions of Dirichlet.Professor Iwasawa reviews the classical results on Dirichlet's L-functions and sketches a proof for some of them. Next he defines generalized Bernoulli numbers and discusses some of their fundamental properties. Continuing, he defines p-adic L-functions, proves their existence and uniqueness, and treats p-adic logarithms and p-adic regulators. He proves a formula of Leopoldt for the values of p-adic L-functions at s=1. The formula was announced in 1964, but a proof has never before been published. Finally, he discusses some applications, especially the strong relationship with cyclotomic fields. 410 0$aAnnals of mathematics studies ;$vNumber 74. 606 $aL-functions 606 $aAlgebraic number theory 610 $aAbelian extension. 610 $aAbsolute value. 610 $aAlgebraic closure. 610 $aAlgebraic number field. 610 $aAlgebraic number theory. 610 $aAlgebraic number. 610 $aAlgebraically closed field. 610 $aArithmetic function. 610 $aClass field theory. 610 $aComplex number. 610 $aConjecture. 610 $aCyclotomic field. 610 $aDirichlet character. 610 $aExistential quantification. 610 $aFinite group. 610 $aInteger. 610 $aL-function. 610 $aMellin transform. 610 $aMeromorphic function. 610 $aMultiplicative group. 610 $aP-adic L-function. 610 $aP-adic number. 610 $aPower series. 610 $aPrime number. 610 $aQuadratic field. 610 $aRational number. 610 $aReal number. 610 $aRoot of unity. 610 $aScientific notation. 610 $aSeries (mathematics). 610 $aSpecial case. 610 $aSubgroup. 610 $aTheorem. 610 $aTopology. 615 0$aL-functions. 615 0$aAlgebraic number theory. 676 $a512/.74 686 $aSI 830$2rvk 700 $aIwasawa$b Kinkichi, $01207597 702 $aIwasawa$b Kenkichi, $4ctb$4https://id.loc.gov/vocabulary/relators/ctb 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910154753503321 996 $aLectures on P-Adic L-Functions. 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Miller 210 1$aTallahassee, Florida :$cU.S. Geological Survey,$d1984. 215 $a1 online resource (iv, 47 pages) $cillustrations, maps 225 1 $aWater-resources investigations report ;$v83-4182 300 $a"Prepared in cooperation with the City of Tampa, Florida." 320 $aIncludes bibliographical references (pages 46-47). 606 $aWater quality$zFlorida$xMathematical models 606 $aWater$xPollution$zFlorida$xMathematical models 606 $aWater$xPollution$xMathematical models$2fast 606 $aWater quality$xMathematical models$2fast 607 $aFlorida$2fast 615 0$aWater quality$xMathematical models. 615 0$aWater$xPollution$xMathematical models. 615 7$aWater$xPollution$xMathematical models. 615 7$aWater quality$xMathematical models. 700 $aFernandez$b Mario$01392349 702 $aGoetz$b Carole L. 702 $aMiller$b Jeffrey E. 712 02$aGeological Survey (U.S.), 712 02$aTampa (Fla.) 801 0$bCOP 801 1$bCOP 801 2$bOCLCO 801 2$bOCLCF 801 2$bOCLCA 801 2$bGPO 906 $aBOOK 912 $a9910713384703321 996 $aEvaluation of future base-flow water-quality conditions in the Hillsborough River, Florida$93527511 997 $aUNINA