Alexander P. Mangerel

activity

20152026

most citedMultiplicative functions that are close to their mean

13 citations · 45 across the 29 of their papers we have counts for

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Showing 2024Show all

3 papers · 1 filter

math.NT2024

On Shusterman's Goldbach-type problem for sign patterns of the Liouville function

Alexander P. Mangerel

Let $λ$ be the Liouville function. Assuming the Generalised Riemann Hypothesis for Dirichlet $L$ -functions (GRH), we show that for every sufficiently large even integer $N$ there a…

math.NT2024

On a Goldbach-type problem for the Liouville function

Alexander P. Mangerel

Let $λ$ denote the Liouville function. We show that for all sufficiently large integers $N$ , the (non-trivial) convolution sum bound $$ \left|\sum_{1 \leq n < N} λ(n) λ(N-n)\right|…

math.NT2024

Large sums of high order characters II

Alexander P. Mangerel, Yichen You

Let $χ$ be a primitive character modulo $q$ , and let $δ > 0$ . Assuming that $χ$ has large order $d$ , for any $d$ th root of unity $α$ we obtain non-trivial upper bounds for the numbe…