New theoretical and numerical investigations of the following two problems
associated with the Dirichlet L-functions L(s; χ) are carried out in this work:
the conjecture on the values L(1/2; χ) and the Extended Riemann Hypothesis
for the function L(s; χ) with a character χ = χ(n) being equal to a Legendre
symbol (n/p), where p is a prime. New rigorous theoretical results give necessary
and sufficient conditions for the validity or refutation of the second conjecture.
Numerical investigations performed with a computer for all p < 500000 confirm
the necessary condition and do not confirm conditions sufficient to its refutation.
An analytic approximation of the numerical distribution is found as well.
Publication language:russian, pages:10
Mathematical problems and theory of numerical methods