Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- 1 Special Values of the Riemann Zeta Function: Some Results and Conjectures
- 2 K-theoretic Background
- 3 Values of the Riemann Zeta Function at the Odd Positive Integers and Iwasawa Theory
- 4 Explicit Reciprocity Law of Bloch–Kato and Exponential Maps
- 5 The Norm Residue Theorem and the Quillen-Lichtenbaum Conjecture
- 6 Regulators and Zeta-functions
- 7 Soulé's Theorem
- 8 Soulé's Regulator Map
- 9 On the Determinantal Approach to the Tamagawa Number Conjecture
- 10 Motivic Polylogarithm and Related Classes
- 11 The Comparison Theorem for the Soulé–Deligne Classes
- 12 Eisenstein Classes, Elliptic Soulé Elements and the ℓ-Adic Elliptic Polylogarithm
- 13 Postscript
- References
1 - Special Values of the Riemann Zeta Function: Some Results and Conjectures
Published online by Cambridge University Press: 05 March 2015
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Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- 1 Special Values of the Riemann Zeta Function: Some Results and Conjectures
- 2 K-theoretic Background
- 3 Values of the Riemann Zeta Function at the Odd Positive Integers and Iwasawa Theory
- 4 Explicit Reciprocity Law of Bloch–Kato and Exponential Maps
- 5 The Norm Residue Theorem and the Quillen-Lichtenbaum Conjecture
- 6 Regulators and Zeta-functions
- 7 Soulé's Theorem
- 8 Soulé's Regulator Map
- 9 On the Determinantal Approach to the Tamagawa Number Conjecture
- 10 Motivic Polylogarithm and Related Classes
- 11 The Comparison Theorem for the Soulé–Deligne Classes
- 12 Eisenstein Classes, Elliptic Soulé Elements and the ℓ-Adic Elliptic Polylogarithm
- 13 Postscript
- References
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- Publisher: Cambridge University PressPrint publication year: 2015
References
[BR01] , and 2001. Irrationalité d'une infinité de valeurs de la fonction zeta aux entiers impairs. (French) [Irrationality of infinitely many values of the zeta function at odd integers]. Invent. Math., 146, no. 1, 193–207.Google Scholar
[BN02] , and 2002. Les nombres de Tamagawa locaux et la conjecture de Bloch et Kato pour les motifs ℚ(m) sur un corps abélien. (French) [Local Tamagawa numbers and the Bloch–Kato conjecture for the motives ℚ(m) over an abelian field]. Ann. Sci. Ecole Norm. Sup., 35, no. 5, 641–672.Google Scholar
[Bl87] 1987. Appendix to Orloff Critical values of certain tensor product L-functions. Invent. Math., (4) 90, no. 1, 181–188.Google Scholar
[Bo74] 1974. Stable real cohomology of arithmetic groups. Ann. Sci. École Norm. Sup., (4) 7, 235–272.Google Scholar
[Bo77] 1977. Cohomologie de SLn et valeurs de fonctions zeta aux points entiers (French). Ann. Scuola Norm. Sup. Pisa Cl. Sci., (4) 4, no. 4, 613–636. (Errata: “Cohomologie de SLn et valeurs de fonctions zeta aux points entiers”. Ann. Scuola Norm. Sup. Pisa Cl. Sci., (4) 7 (1980), no. 2, 373.)Google Scholar
[BK90] , and 1990. L-functions and Tamagawa numbers of motives, The Grothendieck Festschrift, Vol. I. Progr. Math., 86, 333–400. Birkhäuser Boston, Boston, MA.
[Bu02] 2002. The regulators of Beilinson and Borel. CRM Monograph Series, 15. American Mathematical Society, rovidence, RI.
[De79] 1979. Valeurs de fonctions L et périodes d'intégrales (French). With an appendix by N. Koblitz and A. Ogus. Proc. Sympos. Pure Math., XXXIII, Automorphic forms, representations and L-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977), Part 2, 313–346, Amer. Math. Soc., Providence, R. I.
[Fl04] 2004. The equivariant Tamagawa number conjecture: a survey. With an appendix by C. Greither. Contemp. Math., 358, 79–125. Stark–s conjectures: recent work and new directions, Amer. Math. Soc., Providence, RI.
[Fo82] 1982. Sur Certains Types de Representations p-Adiques du Groupe de Galois d'un Corps Local; Construction d'un Anneau de Barsotti-Tate. Ann. of Maths., 2nd Series, 115, no. 3, 529–577.Google Scholar
[Fo92] 1992. Valeurs spéciales des fonctions L des motifs, Astérisque, 206, no. 4, 205–249, Séminaire Bourbaki, Vol. 1991/92, exp. 751.Google Scholar
[HK03] , and 2003. Bloch–Kato conjecture and Main Conjecture of Iwasawa theory for Dirichlet characters. Duke Math. J., 119, no. 3, 393–464.Google Scholar
[Iv85] 1985. The Riemann zeta-function. The theory of the Riemann zeta-function with applications. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York.
[KNF96] , , and 1996. Twisted S-units, p-adic class number formulas, and the Lichtenbaum conjectures. Duke Math. J., 84, no. 3, 679–717.Google Scholar
[Li73] 1973. Values of zeta-functions, étale cohomology, and algebraic K-theory. Algebraic K-theory, II: “Classical” algebraic K-theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Lect. Notes in Math., 342, 489–501. Springer, Berlin.
[Mi71] 1971. Introduction to algebraic K-theory. Annals of Mathematics Studies, no. 72. Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo.
[Ne99] 1999. Algebraic number theory. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 322, xviii–571. Springer-Verlag, Berlin.
[Qu73] 1973. Finite generation of the groups Ki of rings of algebraic integers. Lecture Notes in Math., 341, Springer-Verlag, 179–198.
[Se69] 1969–1970. Facteurs locaux des fonctions zeta des variétés algébriques (définitions et conjectures). Séminaire Delange-Pisot-Poitou. Théorie des nombres, 11, no. 2, exp. no. 19, 1–15.Google Scholar
[We05] 2005. Algebraic K-theory of rings of integers in local and global fields. Handbook of K-theory. 1–2, 139–190, Springer, Berlin.
[We58] 1958–1960. Adéles et groupes algébriques. (French) [Adèles and algebraic groups]Séminaire Bourbaki. 5, exp. no. 186, 249–257.Google Scholar
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