In the last five years there was an essential progress in the development of the
theory of transcendental numbers. A new approach to the arithmetic properties of
values of modular forms and theta-functions was found. First and up to a recent
time there was a unique result of this type established in 1941 by Th. Schneider.
It states that the modular function j{t) has transcendental values at any algebraic
point r of the complex upper-half plane, distinct from the imaginary quadratic
irrationalities. It is well known that the value of the modular function at any
imaginary quadratic argument r with Imr > 0, is an algebraic number.