38050
2014
2014
eng
343
381
39
252
article
Elsevier
San Diego
1
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Conical zeta values and their double subdivision relations
We introduce the concept of a conical zeta value as a geometric generalization of a multiple zeta value in the context of convex cones. The quasi-shuffle and shuffle relations of multiple zeta values are generalized to open cone subdivision and closed cone subdivision relations respectively for conical zeta values. In order to achieve the closed cone subdivision relation, we also interpret linear relations among fractions as subdivisions of decorated closed cones. As a generalization of the double shuffle relation of multiple zeta values, we give the double subdivision relation of conical zeta values and formulate the extended double subdivision relation conjecture for conical zeta values.
Advances in mathematics
10.1016/j.aim.2013.10.022
0001-8708
1090-2082
wos:2014
WOS:000330153100012
Zhang, B (reprint author), Sichuan Univ, Yangtze Ctr Math, Chengdu 610064, Peoples R China., liguo@rutgers.edu; paycha@math.uni-potsdam.de; zhangbin@scu.edu.cn
NSF [DMS 1001855]; NSFC [11071176, 11221101]
Li Guo
Sylvie Paycha
Bin Zhang
eng
uncontrolled
Convex cones
eng
uncontrolled
Conical zeta values
eng
uncontrolled
Smooth cones
eng
uncontrolled
Decorated cones
eng
uncontrolled
Subdivisions
eng
uncontrolled
Multiple zeta values
eng
uncontrolled
Shuffles
eng
uncontrolled
Quasi-shuffles
eng
uncontrolled
Fractions with linear poles
eng
uncontrolled
Shintani zeta values
Institut für Mathematik
Referiert