An algebro-geometric study of special values of hypergeometric functions   ${}_3F_2$
  For certain class of hypergeometric functions ${}_3F_2$ with rational parameters, we give a sufficient condition for the special value at $1$ to be expressed in terms of logarithms of algebraic numbers. We give two proofs, both of which are algebro-geometric and related to higher regulators. 
Masanori Asakura, Noriyuki Otsubo and Tomohide Terasoma
math.NT math.AG math.CA