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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. (AM-74), Volume 74$92785744
997   $aUNINA