Vanishing of Dirichlet L-functions at the central point over function fields

  title={Vanishing of Dirichlet L-functions at the central point over function fields},
  author={Ravi Donepudi and Wanlin Li},
  journal={Rocky Mountain Journal of Mathematics},
We give a geometric criterion for Dirichlet L-functions associated to cyclic characters over the rational function field Fq(t) to vanish at the central point s = 1/2. The idea is based on the observation that vanishing at the central point can be interpreted as the existence of a map from the projective curve associated to the character to some abelian variety over Fq. Using this geometric criterion, we obtain a lower bound on the number of cubic characters over Fq(t) whose L-functions vanish… 

On the Vanishing of Twisted L-Functions of Elliptic Curves

The random matrix model of Katz and Sarnak is used to develop a heuristic for the frequency of vanishing of the twisted Lfunctions LE (l, X), as X runs over the Dirichlet characters of order 3.

Arithmetics, Interrupted

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  • Economics
    Journal of Humanistic Mathematics
  • 2021
I share some of my adventures in mathematical research and homeschooling in the time of COVID-19, where my son is studying for his GCSEs and I am a teacher.



Vanishing of hyperelliptic L-functions at the central point

  • Wanlin Li
  • Mathematics
    Journal of Number Theory
  • 2018

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