Periods of mirrors and multiple zeta values

Author:
Michael E. Hoffman

Journal:
Proc. Amer. Math. Soc. **130** (2002), 971-974

MSC (2000):
Primary 14J32, 11M41; Secondary 05E05

DOI:
https://doi.org/10.1090/S0002-9939-01-06263-3

Published electronically:
October 5, 2001

MathSciNet review:
1873769

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In a recent paper, A. Libgober showed that the multiplicative sequence of Chern classes corresponding to the power series appears in a relation between the Chern classes of certain Calabi-Yau manifolds and the periods of their mirrors. We show that the polynomials can be expressed in terms of multiple zeta values.

**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**

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:
https://doi.org/10.1090/S0002-9939-01-06263-3

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

Published electronically:
October 5, 2001

Communicated by:
Michael Stillman

Article copyright:
© Copyright 2001
American Mathematical Society