F. Ge

activity

20162023

most citedA combinatorial identity and the finite dual of infinite dihedral group algebra

5 citations · 5 across the 2 of their papers we have counts for

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3 papers · 1 filter

math.NT2018

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

Estelle Basor, Fan Ge, Michael O. Rubinstein

We study piecewise polynomial functions $γ_{k} (c)$ that appear in the asymptotics of averages of the divisor sum in short intervals. Specifically, we express these polynomials as the…

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

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…

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

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

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

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