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

##### 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; $$K_3$$
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##### 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A.A.: Letter to Bloch [2] B. Bloch, S.: Higher Regulators, AlgebraicK-theory, and Zeta Functions of Elliptic Curves (unpublished notes) [3] C. Coleman, R.: The dilogarithm and the norm residue symbol.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 (Unpublished notes) [8] K. Katz, N.: Travaux de Dwork.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
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