Abstract
In recent work, we use Dudek’s method together with a result of Zagier to establish an asymptotic formula for the average number of divisors of an irreducible quadratic polynomial of the form \(x^{2}-bx+c\) with b, c integers. In this note, we remark that one can adopt the work of Hooley to derive a more precise asymptotic formula for the case \(x^{2}-bx+c\) with \(b^{2}-4c\) not a square, and as a consequence, re-establish the weaker asymptotic formula given in our recent work by different arguments.
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The author is grateful to the anonymous referee for his/her useful comments, suggestions, and corrections.
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Dongxi Ye is supported by the Natural Science Foundation of China (Grant No. 11901586), the Natural Science Foundation of Guangdong Province (Grant No. 2019A1515011323) and the Sun Yat-sen University Research Grant for Youth Scholars (Grant No. 19lgpy244)
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Ye, D. A remark on the average number of divisors of a quadratic polynomial. Arch. Math. 116, 49–59 (2021). https://doi.org/10.1007/s00013-020-01540-6
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DOI: https://doi.org/10.1007/s00013-020-01540-6