Prime Values of Quadratic Polynomials

This note investigates the prime values of the polynomial $f(t)=qt^2+a$ for any fixed pair of relatively prime integers $ ageq 1$ and $ qgeq 1$ of opposite parity. For a large number $xgeq1$, an asymptotic result of the form $sum_{nleq x^{1/2},, n text{ odd}}Lambda(qn^2+a)gg qx^{1/2}/2varphi(q)$ is achieved for $qll (log x)^b$, where $ bgeq 0 $ is a constant.