Integrals of logarithmic forms on semi-algebraic sets and a generalized   Cauchy formula Part II: generalized Cauchy formula
  This paper is the continuation of the paper arXiv:1509.06950, which is Part I under the same title. In this paper, we prove a generalized Cauchy formula for the integrals of logarithmic forms on products of projective lines, and give an application to the construction of Hodge realization of mixed Tate motives. 
Masaki Hanamura, Kenichiro Kimura and Tomohide Terasoma
math.AG math.CV math.KT math.NT