Nathan Ng

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math.NT2026

Bounds for Mertens Sums

Samuel Broadbent, Andrew Fiori, Habiba Kadiri +2

In this article we provide new bounds for the Mertens sums and products including $\sum_{p \leq x} p^{- 1}$ and $\prod_{p \leq x} (1 - \frac{1}{p})$ which provide superior exponential a…

math.NT2025

An effective version of Chebotarev's density theorem

Sourabhashis Das, Habiba Kadiri, Nathan Ng

Chebotarev's density theorem asserts that the prime ideals are equidistributed among the conjugacy classes of the Galois group of any normal extension of number fields. An effectiv…

math.NT2025

Prime Number Error Terms

Nathan Ng

In 1980 Montgomery made a conjecture about the true order of the error term in the prime number theorem. In 2012 the author made an analogous conjecture for the true order of the s…