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math.NT2019★ 3 cited
The error term in the Sato-Tate theorem of Birch
M. Ram Murty, Neha Prabhu
We establish an error term in the Sato-Tate theorem of Birch. That is, for prime, we show that $\#\{ (a,b) \in \mathbb{F}_q^2 : θ_{a,b}\in I\} =μ_{ST}(I)q^2 + O_r(q^{7/…
math.NT2019
Central limit theorems for elliptic curves and modular forms with smooth weight functions
Stephan Baier, Neha Prabhu, Kaneenika Sinha
The second and third-named authors (arXiv:1705.04115) established a Central Limit Theorem for the error term in the Sato-Tate law for families of modular forms. This method was ada…