Dilogarithms, regulators and \(p\)-adic \(L\)-functions. (English) Zbl 0516.12017

Coleman, Robert F.

Invent. Math. 69, 171-208 (1982).

Reviewer: F. van der Blij

MSC:

11S40	Zeta functions and \(L\)-functions
11S70	\(K\)-theory of local fields
30G06	Non-Archimedean function theory
33B30	Higher logarithm functions
14G20	Local ground fields in algebraic geometry
14G10	Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
19C99	Steinberg groups and \(K_2\)

Keywords:

p-adic L-functions; dilogarithm; Steinberg symbol; \(K_3\)

References:

[1]	Be. Beilenson, A.A.: Letter to Bloch
[2]	B. Bloch, S.: Higher Regulators, AlgebraicK-theory, and Zeta Functions of Elliptic Curves (unpublished notes)
[3]	C. Coleman, R.: The dilogarithm and the norm residue symbol. Bull. Soc. Math. France in press (1982) · Zbl 0493.12019
[4]	D. Dwork, B.: Onp-Adic Differential Equations I, the Frobenius Structure of Differential Equations. Mémoires de la Societé mathemqtique de France9-40, 27-37 (1974)
[5]	G. Goss, D.: Appendix to ?-adic Eisenstein Series for Function Fields (Harvard Ph.D. Thesis 1978)
[6]	Gr. Grauert, H.: Affinoide Uberdeckungen Eindimensionaler Affinoider Räume. IHES Publications Mathématiques34, 5-35 (1968) · Zbl 0197.17302
[7]	Gro. Gross, B.: On the values of ArtinL-functions. (Unpublished notes)
[8]	K. Katz, N.: Travaux de Dwork. Séminaire Bourbaki409, 1-34 (1972)
[9]	Ko. Koblitz, N.: A New proof of Certain Formulas forp-adicL-functions. Duke Math. J.2, 455-468 (1979) · Zbl 0409.12028
[10]	R. Rogers, L.J.: On Function Sum Theorems Connected with the series \(\sum\limits_{n = 1}^\infty {\frac{{x^n }}{{n^2 }}}\) . Proc. London Math. Soc.4, 169-189 (1906) · JFM 37.0428.03
[11]	S. Sandham, H.F.: A Logarithmic Transcendent. J. London Math. Soc.24, 83-91 (1949) · Zbl 0036.32501
[12]	T. Tate, J.: Rigid Analytic Spaces. Invent. Math.12, 257-289 (1971) · Zbl 0212.25601