TY - JOUR
T1 - Unipotent extensions and differential equations (after Bloch-Vlasenko)
AU - Kerr, Matt
N1 - Publisher Copyright:
© 2022, Communications in Number Theory and Physics. All Rights Reserved.
PY - 2022
Y1 - 2022
N2 - S. Bloch and M. Vlasenko recently introduced a theory of motivic Gamma functions, given by periods of the Mellin transform of a geometric variation of Hodge structure. They tie properties of these functions to the monodromy and asymptotic behavior of certain unipotent extensions of the variation. In this article, we further examine their Gamma functions and the related Apéry and Frobenius invariants of a VHS, and establish a relationship to motivic cohomology and solutions to inhomogeneous Picard-Fuchs equations.
AB - S. Bloch and M. Vlasenko recently introduced a theory of motivic Gamma functions, given by periods of the Mellin transform of a geometric variation of Hodge structure. They tie properties of these functions to the monodromy and asymptotic behavior of certain unipotent extensions of the variation. In this article, we further examine their Gamma functions and the related Apéry and Frobenius invariants of a VHS, and establish a relationship to motivic cohomology and solutions to inhomogeneous Picard-Fuchs equations.
KW - Apéry constants
KW - Frobenius constants
KW - Motivic cohomology
KW - Motivic gamma functions
KW - Normal functions
KW - Periods
KW - Picar-dfuchs equations
KW - Variations of hodge structure
UR - http://www.scopus.com/inward/record.url?scp=85140744017&partnerID=8YFLogxK
U2 - 10.4310/CNTP.2022.v16.n4.a5
DO - 10.4310/CNTP.2022.v16.n4.a5
M3 - Article
AN - SCOPUS:85140744017
SN - 1931-4523
VL - 16
SP - 801
EP - 849
JO - Communications in Number Theory and Physics
JF - Communications in Number Theory and Physics
IS - 4
ER -