Problems related to arithmetic properties of linear forms in various irrational and
transcendental numbers, lower bounds for these linear forms, and approximation by
rational fractions with bounded denominators are very popular in transcendence
theory. We consider a new symmetric integral construction and prove a series of new
lower bounds for joint approximations of certain values of the functions
. Namely,
the integral construction of such a type allows us to obtain new bounds for the linear forms
with special
values of
,
.
Keywords
joint approximations, logarithmic function, arctangent
function, linear form