ON SIL VERMAN'S ESTIMATE OF REGULATORS

Abstract

Silverman proved that the size of the regulator of the algebraic number field grows at least with some power of the logarithm ofthe absolute value of the dicriminant, multiplied by some constant depending only on the degree of the field. He also stated that the exponent he obtained may be the best. But it is not the best in many cases and we can replace it by better one.