Prime Values of Quadratic Polynomials

N. A. Carella

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arXiv · 2009.00417

Prime Values of Quadratic Polynomials

N. A. Carella

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Abstract

This note investigates the prime values of the polynomial $f(t)=qt^2+a$ for any fixed pair of relatively prime integers $ a\geq 1$ and $ q\geq 1$ of opposite parity. For a large number $x\geq1$, an asymptotic result of the form $\sum_{n\leq x^{1/2},\, n \text{ odd}}\Lambda(qn^2+a)\gg qx^{1/2}/2\varphi(q)$ is achieved for $q\ll (\log x)^b$, where $ b\geq 0 $ is a constant.

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BibTeX RIS

N. A. Carella. 2020-08-31. Prime Values of Quadratic Polynomials. https://arxiv.org/abs/2009.00417

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