Abstract: | The fundamental result of the paper is the following theorem: suppose that the Riemann conjecture is valid for the Dedekind ζ-functions of all fields Then there exists a constant C>0 such that on the interval p≤x one can find at least Cx log−1 x prime numbers p for which h(5p2)=2. Here h(d) is the number of proper equivalence classes of primitive binary quadratic forms of discriminant d. In addition, it is proved that . For these sequence of discriminants of a special form with increasing square-free part, one has obtained a nontrivial estimate from above for the number of classes. Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 160, pp. 72–81, 1987. |