Deligne periods of mixed motives, 𝐾-theory and the entropy of certain ℤⁿ-actions

Deninger, Christopher

doi:10.1090/S0894-0347-97-00228-2

Deligne periods of mixed motives, $K$-theory and the entropy of certain $\mathbb {Z}^n$-actions
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by Christopher Deninger

J. Amer. Math. Soc. 10 (1997), 259-281

DOI: https://doi.org/10.1090/S0894-0347-97-00228-2

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References

Lars V. Ahlfors, Complex analysis: An introduction of the theory of analytic functions of one complex variable, 2nd ed., McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0188405
A. A. Beĭlinson, Higher regulators and values of $L$-functions, Current problems in mathematics, Vol. 24, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1984, pp. 181–238 (Russian). MR 760999
A. A. Beĭlinson, Higher regulators of modular curves, Applications of algebraic $K$-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983) Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 1–34. MR 862627, DOI 10.1090/conm/055.1/862627
B. J. Birch and W. Kuyk (eds.), Modular functions of one variable. IV, Lecture Notes in Mathematics, Vol. 476, Springer-Verlag, Berlin-New York, 1975. MR 0376533
S. Bloch and D. Grayson, $K_2$ and $L$-functions of elliptic curves: computer calculations, Applications of algebraic $K$-theory to algebraic geometry and number theory, Part I, II (Boulder, Colo., 1983) Contemp. Math., vol. 55, Amer. Math. Soc., Providence, RI, 1986, pp. 79–88. MR 862631, DOI 10.1090/conm/055.1/862631
David W. Boyd, Speculations concerning the range of Mahler’s measure, Canad. Math. Bull. 24 (1981), no. 4, 453–469. MR 644535, DOI 10.4153/CMB-1981-069-5
D.W. Boyd, Explicit formulas for Mahler’s measure. Preprint 1996.
Pierre Deligne, Théorie de Hodge. II, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 5–57 (French). MR 498551
P. Deligne, Valeurs de fonctions $L$ et périodes d’intégrales, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 313–346 (French). With an appendix by N. Koblitz and A. Ogus. MR 546622
P. Deligne, Le groupe fondamental de la droite projective moins trois points, Galois groups over $\textbf {Q}$ (Berkeley, CA, 1987) Math. Sci. Res. Inst. Publ., vol. 16, Springer, New York, 1989, pp. 79–297 (French). MR 1012168, DOI 10.1007/978-1-4613-9649-9_{3}
Christopher Deninger, Higher regulators and Hecke $L$-series of imaginary quadratic fields. I, Invent. Math. 96 (1989), no. 1, 1–69. MR 981737, DOI 10.1007/BF01393970
C. Deninger, Extensions of motives associated to symmetric powers of elliptic curves and to Hecke characters of imaginary quadratic fields. Preprint 1995.
C. Deninger, On extensions of mixed motives. Preprint 1995.
Christopher Deninger and Kay Wingberg, On the Beĭlinson conjectures for elliptic curves with complex multiplication, Beĭlinson’s conjectures on special values of $L$-functions, Perspect. Math., vol. 4, Academic Press, Boston, MA, 1988, pp. 249–272. MR 944996
A. Huber, Mixed motives and their realizations in derived categories. Springer LNM 1604, 1995.
M. Rapoport, N. Schappacher, and P. Schneider (eds.), Beilinson’s conjectures on special values of $L$-functions, Perspectives in Mathematics, vol. 4, Academic Press, Inc., Boston, MA, 1988. MR 944987
Uwe Jannsen, Mixed motives and algebraic $K$-theory, Lecture Notes in Mathematics, vol. 1400, Springer-Verlag, Berlin, 1990. With appendices by S. Bloch and C. Schoen. MR 1043451, DOI 10.1007/BFb0085080
Uwe Jannsen, Steven Kleiman, and Jean-Pierre Serre (eds.), Motives, Proceedings of Symposia in Pure Mathematics, vol. 55, American Mathematical Society, Providence, RI, 1994. MR 1265518, DOI 10.1090/pspum/055.1
G. Kings, Extensions of motives of modular forms. To appear in Math. Ann.
Douglas Lind, Klaus Schmidt, and Tom Ward, Mahler measure and entropy for commuting automorphisms of compact groups, Invent. Math. 101 (1990), no. 3, 593–629. MR 1062797, DOI 10.1007/BF01231517
James S. Milne, Étale cohomology, Princeton Mathematical Series, No. 33, Princeton University Press, Princeton, N.J., 1980. MR 559531
Patrice Philippon, Critères pour l’indépendance algébrique, Inst. Hautes Études Sci. Publ. Math. 64 (1986), 5–52 (French). MR 876159
M. Rapoport, N. Schappacher, and P. Schneider (eds.), Beilinson’s conjectures on special values of $L$-functions, Perspectives in Mathematics, vol. 4, Academic Press, Inc., Boston, MA, 1988. MR 944987
Gary Alan Ray, Relations between Mahler’s measure and values of $L$-series, Canad. J. Math. 39 (1987), no. 3, 694–732. MR 905752, DOI 10.4153/CJM-1987-034-0
K. Schmidt, Dynamical systems of algebraic origin. Progress in Math. 128, Basel 1995.
Norbert Schappacher and Anthony J. Scholl, The boundary of the Eisenstein symbol, Math. Ann. 290 (1991), no. 2, 303–321. MR 1109636, DOI 10.1007/BF01459247
Peter Schneider, Introduction to the Beĭlinson conjectures, Beĭlinson’s conjectures on special values of $L$-functions, Perspect. Math., vol. 4, Academic Press, Boston, MA, 1988, pp. 1–35. MR 944989
Anthony J. Scholl, Remarks on special values of $L$-functions, $L$-functions and arithmetic (Durham, 1989) London Math. Soc. Lecture Note Ser., vol. 153, Cambridge Univ. Press, Cambridge, 1991, pp. 373–392. MR 1110402, DOI 10.1017/CBO9780511526053.016
A. J. Scholl, Height pairings and special values of $L$-functions, Motives (Seattle, WA, 1991) Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp. 571–598. MR 1265545, DOI 10.1090/pspum/055.1/1265545
C. J. Smyth, On measures of polynomials in several variables, Bull. Austral. Math. Soc. 23 (1981), no. 1, 49–63. MR 615132, DOI 10.1017/S0004972700006894