# On a problem of Hoffstein and Kontorovich.

@article{Dunn2020OnAP, title={On a problem of Hoffstein and Kontorovich.}, author={Alexander Dunn}, journal={arXiv: Number Theory}, year={2020} }

Let $\pi$ be a cuspidal automorphic representation of $\operatorname{GL}_2(\mathbb{A}_{\mathbb{Q}})$ and $d$ be a fundamental discriminant. Hoffstein and Kontorovich ask for a bound on the least $|d|$ (if it exists) such that the central value $L(1/2, \pi \otimes \chi_d) \neq 0$. The bound should be given in terms of the weight, Laplace eigenvalue and/or level of $\pi$.
Let $f$ be a holomorphic twist-minimal newform of even weight $\ell$, odd cubefree level $N$, and trivial nebentypus. When…

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