• 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
Abstract For two real characters ψ,ψ′ of conductor dividing 8 define \[ Z(s, w; \psi , \psi ') := \zeta _2(2s+2w-1) \sum _{d \text { odd}} \frac {L_2(s, \chi _d\psi ) \psi '(d)}{d^w} \] where $\chi
The first non-vanishing quadratic twist of an automorphic L-series
Let pi be an automorphic representation on GL(r, A_Q) for r=1, 2, or 3. Let d be a fundamental discriminant and chi_d the corresponding quadratic Dirichlet character. We consider the question of the
SUMS OF TWISTED GL ( 3 ) AUTOMORPHIC L-FUNCTIONS
Let F be a number field and π be an automorphic representation on GLr (AF ). In this paper we consider weighted sums of quadratic twists of the L-function for π , ∑ d L(s, π, χd ) a(s, π, d) Nd −w ,
Growth and nonvanishing of restricted Siegel modular forms arising as Saito-Kurokawa lifts
<abstract abstract-type="TeX"><p> We study the analytic behavior of the restriction of a Siegel modular form to $\Bbb{H}\times\Bbb{H}$ in the case that the Siegel form is a Saito-Kurokawa lift. A
On the modularity of elliptic curves over Q
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"
TLDR
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.
A Theorem on Analytic Continuation of Functions in Several Variables
0 xX = Xx ; _x < ye < ??, K = 1, **k where (x?, ... , x) is an arbitrary point of S. A tube is an (open) domain if and only if its basis is a domain. We shall say that a tube T' lies within a tube T
Non-vanishing of quadratic twists of modular L-functions
;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
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.
...
...