## Beukers' integral and the non-quadraticity measure for the values of logarithm at rational points

J. Math. Sci. Univ. Tokyo
Vol. 11 (2004), No. 4, Page 455--501.

Sato, Susumu
Beukers' integral and the non-quadraticity measure for the values of logarithm at rational points
We have a non-quadraticity measure estimation for the values of logarithm at various rational points by using rather general Beukers' double integrals.\ To investigate an asymptotic analysis for the integral,\ we need the two-dimensional version of the saddle point method,\ which is called $\C^2$-saddle point method.\ This is a generalization of a part of Hata's result [6].