F. Ge

activity

20092023

most citedSome multidimensional integrals in number theory and connections with the Painlevé V equation

9 citations · 19 across the 14 of their papers we have counts for

collaborators

Showing 2016Show all

4 papers · 1 filter

math.NT2016

Note on the index conjecture in zero-sum theory and its connection to a Dedekind-type sum

Fan Ge

Let $S = (a_{1}) \dots (a_{k})$ be a minimal zero-sum sequence over a finite cyclic group $G$ . The index conjecture states that if $k = 4$ and $g cd (∣ G ∣, 6) = 1$ , then $S$ has index 1. In this…

math.NT2016★ 3 cited

On the index conjecture in zero-sum theory: singular case

Fan Ge

Let $S = (a_{1}) \dots (a_{k})$ be a minimal zero-sum sequence over a finite cyclic group $G$ . The index conjecture states that if $k = 4$ and $g cd (∣ G ∣, 6) = 1$ , then $S$ has index $1$ . In th…

math.NT2016

Conditional estimates on small distances between ordinates of zeros of $ζ (s)$ and $ζ^{'} (s)$

Fan Ge

Let $β^{'} + i γ^{'}$ be a zero of $ζ^{'} (s)$ . In \cite{GYi} Garaev and Yıldırım proved that there is a zero $β + iγ$ of $ζ (s)$ with $γ^{'} - γ ≪ ∣ β^{'} - 1/2∣$ . Assuming RH, we improve this bou…

math.NT2016

On a permutation problem for finite abelian groups

Fan Ge, Zhi-Wei Sun

Let $G$ be a finite additive abelian group with exponent $n > 1$ , and let $a_{1}, \dots, a_{n - 1} \in G$ . We show that there is a permutation $σ \in S_{n - 1}$ such that all the elements $sa…

Note on the index conjecture in zero-sum theory and its connection to a Dedekind-type sum

On the index conjecture in zero-sum theory: singular case

Conditional estimates on small distances between ordinates of zeros of ζ(s) and ζ′(s)

On a permutation problem for finite abelian groups

Conditional estimates on small distances between ordinates of zeros of $ζ (s)$ and $ζ^{'} (s)$