• Corpus ID: 220525892

# 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…

## References

SHOWING 1-10 OF 36 REFERENCES

### Multiple Dirichlet Series for Affine Weyl Groups

Let $W$ be the Weyl group of a simply-laced affine Kac-Moody Lie group, excepting $\tilde{A}_n$ for $n$ even. We construct a multiple Dirichlet series $Z(x_1, \ldots x_{n+1})$, meromorphic in a

### Subconvexity for a double Dirichlet series

• V. Blomer
• Mathematics
Compositio Mathematica
• 2010

### On the modularity of elliptic curves over Q

• Mathematics
• 1999
In this paper, building on work of Wiles [Wi] and of Wiles and one of us (R.T.) [TW], we will prove the following two theorems (see §2.2). Theorem A. If E/Q is an elliptic curve, then E is modular.

### Erratum: "On the computation of local components of a newform"

• Mathematics
Math. Comput.
• 2015
A cuspidal newform for Γ1(N) with weight k ≥ 2 and character e is computed using modular symbols and the corresponding automorphic representation of the adele group GL2(AQ) is defined.

### Non-vanishing of quadratic twists of modular L-functions

• Mathematics
• 1998
;kƒhave been the subject of much study, both because of their intrinsicinterest and because of the prominent role they have played inKolyvagin’s work on the Birch and Swinnerton-Dyer Conjecture

### Weyl Group Multiple Dirichlet Series I

• Mathematics
• 2006
Given a root system Φ of rank r and a global field F containing the n-th roots of unity, it is possible to define a Weyl group multiple Dirichlet series whose coefficients are n-th order Gauss sums.

### Multiple Dirichlet Series and Moments of Zeta and L-Functions

• Mathematics
Compositio Mathematica
• 2003
This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward