Lectures on P-Adic L-Functions. (AM-74), Volume 74 / / Kinkichi Iwasawa.
An 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...
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| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2016] ©1972 |
| Year of Publication: | 2016 |
| Language: | English |
| Series: | Annals of Mathematics Studies ;
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Iwasawa, Kinkichi, author. aut http://id.loc.gov/vocabulary/relators/aut Lectures on P-Adic L-Functions. (AM-74), Volume 74 / Kinkichi Iwasawa. Princeton, NJ : Princeton University Press, [2016] ©1972 1 online resource (112 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 74 Frontmatter -- PREFACE -- CONTENTS -- §1. DIRICHLET'S L-FUNCTIONS -- §2. GENERALIZED BERNOULLI NUMBERS -- §3. p-ADIC L-FUNCTIONS -- §4. p-ADIC LOGARITHMS AND p-ADIC REGULATORS -- §5. CALCULATION OF Lp (1; χ) -- §6. AN ALTERNATE METHOD -- §7. SOME APPLICATIONS -- APPENDIX -- BIBLIOGRAPHY restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star An 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Algebraic number theory. L-functions. MATHEMATICS / Number Theory. bisacsh Abelian extension. Absolute value. Algebraic closure. Algebraic number field. Algebraic number. Algebraically closed field. Arithmetic function. Class field theory. Complex number. Conjecture. Cyclotomic field. Dirichlet character. Existential quantification. Finite group. Integer. L-function. Mellin transform. Meromorphic function. Multiplicative group. P-adic L-function. P-adic number. Power series. Prime number. Quadratic field. Rational number. Real number. Root of unity. Scientific notation. Series (mathematics). Special case. Subgroup. Theorem. Topology. Iwasawa, Kenkichi, contributor. ctb https://id.loc.gov/vocabulary/relators/ctb Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691081120 https://doi.org/10.1515/9781400881703 https://www.degruyter.com/isbn/9781400881703 Cover https://www.degruyter.com/document/cover/isbn/9781400881703/original |
| language |
English |
| format |
eBook |
| author |
Iwasawa, Kinkichi, Iwasawa, Kinkichi, |
| spellingShingle |
Iwasawa, Kinkichi, Iwasawa, Kinkichi, Lectures on P-Adic L-Functions. (AM-74), Volume 74 / Annals of Mathematics Studies ; Frontmatter -- PREFACE -- CONTENTS -- §1. DIRICHLET'S L-FUNCTIONS -- §2. GENERALIZED BERNOULLI NUMBERS -- §3. p-ADIC L-FUNCTIONS -- §4. p-ADIC LOGARITHMS AND p-ADIC REGULATORS -- §5. CALCULATION OF Lp (1; χ) -- §6. AN ALTERNATE METHOD -- §7. SOME APPLICATIONS -- APPENDIX -- BIBLIOGRAPHY |
| author_facet |
Iwasawa, Kinkichi, Iwasawa, Kinkichi, Iwasawa, Kenkichi, Iwasawa, Kenkichi, |
| author_variant |
k i ki k i ki |
| author_role |
VerfasserIn VerfasserIn |
| author2 |
Iwasawa, Kenkichi, Iwasawa, Kenkichi, |
| author2_variant |
k i ki k i ki |
| author2_role |
MitwirkendeR MitwirkendeR |
| author_sort |
Iwasawa, Kinkichi, |
| title |
Lectures on P-Adic L-Functions. (AM-74), Volume 74 / |
| title_full |
Lectures on P-Adic L-Functions. (AM-74), Volume 74 / Kinkichi Iwasawa. |
| title_fullStr |
Lectures on P-Adic L-Functions. (AM-74), Volume 74 / Kinkichi Iwasawa. |
| title_full_unstemmed |
Lectures on P-Adic L-Functions. (AM-74), Volume 74 / Kinkichi Iwasawa. |
| title_auth |
Lectures on P-Adic L-Functions. (AM-74), Volume 74 / |
| title_alt |
Frontmatter -- PREFACE -- CONTENTS -- §1. DIRICHLET'S L-FUNCTIONS -- §2. GENERALIZED BERNOULLI NUMBERS -- §3. p-ADIC L-FUNCTIONS -- §4. p-ADIC LOGARITHMS AND p-ADIC REGULATORS -- §5. CALCULATION OF Lp (1; χ) -- §6. AN ALTERNATE METHOD -- §7. SOME APPLICATIONS -- APPENDIX -- BIBLIOGRAPHY |
| title_new |
Lectures on P-Adic L-Functions. (AM-74), Volume 74 / |
| title_sort |
lectures on p-adic l-functions. (am-74), volume 74 / |
| series |
Annals of Mathematics Studies ; |
| series2 |
Annals of Mathematics Studies ; |
| publisher |
Princeton University Press, |
| publishDate |
2016 |
| physical |
1 online resource (112 p.) Issued also in print. |
| contents |
Frontmatter -- PREFACE -- CONTENTS -- §1. DIRICHLET'S L-FUNCTIONS -- §2. GENERALIZED BERNOULLI NUMBERS -- §3. p-ADIC L-FUNCTIONS -- §4. p-ADIC LOGARITHMS AND p-ADIC REGULATORS -- §5. CALCULATION OF Lp (1; χ) -- §6. AN ALTERNATE METHOD -- §7. SOME APPLICATIONS -- APPENDIX -- BIBLIOGRAPHY |
| isbn |
9781400881703 9783110494914 9783110442496 9780691081120 |
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Q - Science |
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QA - Mathematics |
| callnumber-label |
QA247 |
| callnumber-sort |
QA 3247 I95 41972EB |
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https://doi.org/10.1515/9781400881703 https://www.degruyter.com/isbn/9781400881703 https://www.degruyter.com/document/cover/isbn/9781400881703/original |
| illustrated |
Not Illustrated |
| dewey-hundreds |
500 - Science |
| dewey-tens |
510 - Mathematics |
| dewey-ones |
512 - Algebra |
| dewey-full |
512/.74 |
| dewey-sort |
3512 274 |
| dewey-raw |
512/.74 |
| dewey-search |
512/.74 |
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10.1515/9781400881703 |
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979579082 |
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Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
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Lectures on P-Adic L-Functions. (AM-74), Volume 74 / |
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