3 citations · 3 across the 11 of their papers we have counts for
17 papers · 1 filter
On a conjecture of Goldmakher
Alexander P. Mangerel
We construct a -bounded completely multiplicative function whose logarithmically-averaged partial sums satisfy $$ \limsup_{x \rightarrow \infty} \frac{\left|\sum_{n \leq x}…
A Halász-type asymptotic formula for logarithmic means and its consequences
Oleksiy Klurman, Alexander P. Mangerel
We establish an asymptotic formula for the logarithmic mean value of a 1-bounded multiplicative function that is sharp in many cases of interest. We derive from it a variety of app…
Sharp bounds for maximal sums of odd order Dirichlet characters
Alexander P. Mangerel
Let be fixed and odd, and for large let be a primitive Dirichlet character modulo of order . Conditionally on GRH we improve the existing upper bounds in…
On a rigidity property for quadratic Gauss sums
Alexander P. Mangerel
Let be a large prime and let . We prove that if is a -valued completely multiplicative function, such that the exponential sums $$ S_f(a) := \sum_{1 \leq n…
On Shusterman's Goldbach-type problem for sign patterns of the Liouville function
Alexander P. Mangerel
Let be the Liouville function. Assuming the Generalised Riemann Hypothesis for Dirichlet -functions (GRH), we show that for every sufficiently large even integer there a…
On a Goldbach-type problem for the Liouville function
Alexander P. Mangerel
Let denote the Liouville function. We show that for all sufficiently large integers , the (non-trivial) convolution sum bound $$ \left|\sum_{1 \leq n < N} λ(n) λ(N-n)\right|…