Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Periods of mirrors and multiple zeta values

Author(s): Michael E. Hoffman
Journal: Proc. Amer. Math. Soc. 130 (2002), 971-974.
MSC (2000): Primary 14J32, 11M41; Secondary 05E05
Posted: October 5, 2001
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: In a recent paper, A. Libgober showed that the multiplicative sequence $\{Q_i(c_1,\dots,c_i)\}$ of Chern classes corresponding to the power series $Q(z)=\Gamma(1+z)^{-1}$ appears in a relation between the Chern classes of certain Calabi-Yau manifolds and the periods of their mirrors. We show that the polynomials $Q_i$ can be expressed in terms of multiple zeta values.


References:

1.
D. J. Broadhurst and K. Kreimer, Association of multiple zeta values with positive knots via Feynman diagrams up to 9 loops, Phys. Lett. B 393 (1997), 403-412. MR 98g:11101
2.
I. M. Gessel, Multipartite P-partitions and inner products of skew Schur functions, Combinatorics and Algebra, Contemp. Math. vol. 34, Amer. Math. Soc., Providence, RI, 1984, pp. 289-301. MR 86k:05007
3.
M. E. Hoffman, Multiple harmonic series, Pacific J. Math. 152 (1992), 275-290. MR 92i:11089
4.
M. E. Hoffman, The algebra of multiple harmonic series, J. Algebra 194 (1997), 477-495. MR 99e:11119
5.
T. Q. T. Le and J. Murakami, Kontsevich's integral for the Homfly polynomial and relations between values of the multiple zeta functions, Topology Appl. 62 (1995), 193-206. MR 96c:57017
6.
A. Libgober, Chern classes and the periods of mirrors, Math. Res. Lett. 6 (1999), 141-149. MR 2000h:32017
7.
I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd ed., Oxford University Press, New York, 1995. MR 96h:05207
8.
D. Zagier, Values of zeta functions and their applications, First European Congress of Mathematics, vol. 2, Birkhauser, Boston, 1994, pp. 497-512. MR 96k:11110

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 14J32, 11M41, 05E05

Retrieve articles in all Journals with MSC (2000): 14J32, 11M41, 05E05


Additional Information:

Michael E. Hoffman
Affiliation: United States Naval Academy, Annapolis, Maryland 21402
Email: meh@usna.edu

DOI: 10.1090/S0002-9939-01-06263-3
PII: S 0002-9939(01)06263-3
Keywords: Mirror symmetry, multiple zeta values, gamma function
Received by editor(s): November 23, 1999
Received by editor(s) in revised form: October 18, 2000
Posted: October 5, 2001
Communicated by: Michael Stillman
Copyright of article: Copyright 2001, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google