One motivation to consider this form comes from (9.11) and Goncharov's explicit formulas for regulators (cf ,
Eta invariants, signature defects of cusps, and values of Lfunctions, Ann. of Math, vol.118, issue.2, pp.131-177, 1983. ,
Topological polylogarithms and p-adic interpolation of L-values of totally real fields, Math. Ann, vol.371, issue.3-4, pp.1449-1495, 2018. ,
Heat kernels and Dirac operators. Grundlehren Text Editions, 2004. ,
The elliptic polylogarithm, Motives, vol.55, pp.123-190, 1991. ,
Higher regulators and values of L-functions, Current problems in mathematics, vol.24, pp.181-238, 1984. ,
Remarks on the index theorem for families of Dirac operators on manifolds with boundary, Differential geometry, vol.52, pp.59-83, 1991. ,
Analytic torsion and holomorphic determinant bundles. I. Bott-Chern forms and analytic torsion, Comm. Math. Phys, vol.115, issue.1, pp.49-78, 1988. ,
Transgressed Euler classes of SL(2n, Z) vector bundles, adiabatic limits of eta invariants and special values of L-functions, Ann. Sci. École Norm. Sup, vol.25, issue.4, pp.335-391, 1992. ,
On the critical values of Hecke L-series, Ann. of Math, vol.124, issue.2, pp.23-63, 1986. ,
Toric modular forms and nonvanishing of L-functions, J. Reine Angew. Math, vol.539, pp.149-165, 2001. ,
Toric varieties and modular forms, Invent. Math, vol.144, issue.2, pp.297-325, 2001. ,
Differential forms in algebraic topology, Graduate Texts in Mathematics, vol.82, 1982. ,
Beilinson-Kato elements in K 2 of modular curves, Acta Arith, vol.134, issue.3, pp.283-298, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00561919
Valeurs aux entiers négatifs des fonctions zêta et fonctions zêta p-adiques, Invent. Math, vol.51, issue.1, pp.29-59, 1979. ,
Integral Eisenstein cocycles on GLn, I: Sczech's cocycle and p-adic L-functions of totally real fields, Camb. J. Math, vol.2, issue.1, pp.49-90, 2014. ,
II: Shintani's method, Integral Eisenstein cocycles on GLn, vol.90, issue.2, pp.435-477, 2015. ,
Elliptic functions according to Eisenstein and Kronecker: an update, Eur. Math. Soc. Newsl, issue.101, pp.8-14, 2016. ,
A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds, Ann. of Math, vol.45, issue.2, pp.747-752, 1944. ,
Algébricité de valeurs spéciales de fonctions L, Invent. Math, vol.95, issue.1, pp.161-205, 1989. ,
L-functions of elliptic curves with complex multiplication, I. Acta Arith, vol.17, pp.287-301, 1970. ,
, Automorphic forms, representations and Lfunctions (Proc. Sympos. Pure Math, vol.2, pp.313-346, 1977.
Values of abelian L-functions at negative integers over totally real fields, Invent. Math, vol.59, issue.3, pp.227-286, 1980. ,
Arithmetic Eisenstein classes on the Siegel space: some computations, Number fields and function fields-two parallel worlds, vol.239, pp.133-166, 2005. ,
Eisenstein cocycles over imaginary quadratic fields and special values of L-functions, J. Number Theory, vol.204, pp.497-531, 2019. ,
Superconnections, theta series, and period domains, Adv. Math, vol.329, pp.555-589, 2018. ,
The Thom class of Mathai and Quillen and probability theory, Stochastic analysis and applications, vol.26, pp.111-122, 1989. ,
, Handbook of K-theory, vol.1, pp.295-349, 2005.
Polylogarithms for GL 2 over totally real fields, 2016. ,
Special values of Hecke L-functions and abelian integrals, Workshop Bonn, vol.1111, pp.17-49, 1984. ,
Some results on the Eisenstein cohomology of arithmetic subgroups of GLn, Cohomology of arithmetic groups and automorphic forms, vol.1447, pp.85-153, 1989. ,
An introduction to the theory of numbers, 2008. ,
?-series and invariant theory, Automorphic forms, representations and L-functions (Proc. Sympos, pp.275-285, 1977. ,
A short history on investigation of the special values of zeta and L-functions of totally real number fields, Automorphic forms and zeta functions, pp.198-233, 2006. ,
A function on the upper half space which is analogous to the imaginary part of log ?(z), J. Reine Angew. Math, vol.373, pp.148-165, 1987. ,
p-adic Hodge theory and values of zeta functions of modular forms, Cohomologies p-adiques et applications arithmétiques, vol.295, pp.117-290, 2004. ,
über die Werte der Dedekindschen Zetafunktion, Math. Ann, vol.145, pp.265-272, 1961. ,
Seesaw dual reductive pairs, Automorphic forms of several variables, vol.46, pp.244-268, 1983. ,
Intersection numbers of cycles on locally symmetric spaces and Fourier coefficients of holomorphic modular forms in several complex variables, Inst. Hautes Études Sci. Publ. Math, issue.71, pp.121-172, 1990. ,
Superconnections, Thom classes, and equivariant differential forms, Topology, vol.25, issue.1, pp.85-110, 1986. ,
Signature defects of cusps of Hilbert modular varieties and values of L-series at s = 1, J. Differential Geom, vol.20, issue.1, pp.55-119, 1984. ,
Some Eisenstein cohomology classes for the integral unimodular group, Proceedings of the International Congress of Mathematicians, vol.1, pp.690-696, 1994. ,
Dedekindsummen mit elliptischen Funktionen, Invent. Math, vol.76, issue.3, pp.523-551, 1984. ,
Eisenstein cocycles for GL 2 Q and values of L-functions in real quadratic fields, Comment. Math. Helv, vol.67, issue.3, pp.363-382, 1992. ,
Eisenstein group cocycles for GLn and values of L-functions, Invent. Math, vol.113, issue.3, pp.581-616, 1993. ,
On evaluation of zeta functions of totally real algebraic number fields at non-positive integers, J. Fac. Sci. Univ. Tokyo Sect. IA Math, vol.23, issue.2, pp.393-417, 1976. ,
Über die analytische Theorie der quadratischen Formen, III. Ann. of Math, vol.38, issue.2, pp.212-291, 1937. ,
Advanced analytic number theory, Tata Institute of Fundamental Research Studies in Mathematics. Tata Institute of Fundamental Research, vol.9, 1980. ,
, Gesammelte Abhandlungen. IV. Springer Collected Works in Mathematics, 2015.
La classe d'Euler réelle d'un fibré vectoriel à groupe structural SLn(Z) est nulle, C. R. Acad. Sci. Paris Sér. A-B, vol.281, issue.1, pp.17-18, 1975. ,
Elliptic functions according to Eisenstein and Kronecker, Classics in Mathematics, 1999. ,
Séries d'Eisenstein, intégrales toroïdales et une formule de Hecke, Enseign. Math, issue.2, pp.93-135, 1985. ,
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