Lectures on P-Adic L-Functions
Seiten
1972
Princeton University Press (Verlag)
978-0-691-08112-0 (ISBN)
Princeton University Press (Verlag)
978-0-691-08112-0 (ISBN)
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These are notes of lectures given at Princeton University during the fall semester of 1969. The notes present an introduction to p-adic L-functions originated in Kubota-Leopoldt {10} as p-adic analogues of classical L-functions of Dirichlet.
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.
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.
*Frontmatter, pg. i*PREFACE, pg. v*CONTENTS, pg. vii* 1. DIRICHLET'S L-FUNCTIONS, pg. 1* 2. GENERALIZED BERNOULLI NUMBERS, pg. 7* 3. p-ADIC L-FUNCTIONS, pg. 17* 4. p-ADIC LOGARITHMS AND p-ADIC REGULATORS, pg. 36* 5. CALCULATION OF Lp (1; chi), pg. 43* 6. AN ALTERNATE METHOD, pg. 66* 7. SOME APPLICATIONS, pg. 88*APPENDIX, pg. 100*BIBLIOGRAPHY, pg. 105
Erscheint lt. Verlag | 21.7.1972 |
---|---|
Reihe/Serie | Annals of Mathematics Studies |
Verlagsort | New Jersey |
Sprache | englisch |
Maße | 152 x 229 mm |
Gewicht | 170 g |
Themenwelt | Mathematik / Informatik ► Mathematik |
ISBN-10 | 0-691-08112-3 / 0691081123 |
ISBN-13 | 978-0-691-08112-0 / 9780691081120 |
Zustand | Neuware |
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