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math.NT2023
Arithmetic rank bounds for abelian varieties over function fields
Félix Baril Boudreau, Jean Gillibert, Aaron Levin
It follows from the Grothendieck-Ogg-Shafarevich formula that the rank of an abelian variety (with trivial trace) defined over the function field of a curve is bounded by a quantit…
math.NT2023
Mean values of long Dirichlet polynomials with divisor coefficients
Fatma Cicek, Alia Hamieh, Nathan Ng
In this article, we prove an asymptotic formula for the mean value of long smoothed Dirichlet polynomials with divisor coefficients. Our result has a main term that includes all lo…