arXiv subjects

Alia Hamieh

Publications and source records attributed to Alia Hamieh.

22 records · Page 2Linked to original sources

arXiv2016

Determining Hilbert Modular Forms by Central Values of Rankin-Selberg Convolutions: The Level Aspect

In this paper, we prove that a primitive Hilbert cusp form $\mathbf{g}$ is uniquely determined by the central values of the Rankin-Selberg $L$-functions $L(\mathbf{f}\otimes\mathbf{g}, \frac{1}{2})$, where $\mathbf{f}$ runs through all primitive Hilbert cusp forms of level $\mathfrak{q}$ for infinitely many prime ideals $\mathfrak{q}$. This result is a generalization of a theorem of Luo to the setting of totally real number fields.

math.NT↗

arXiv2016

Determining Hilbert Modular Forms by Central Values of Rankin-Selberg Convolutions: The Weight Aspect

The purpose of this paper is to prove that a primitive Hilbert cusp form $\mathbf{g}$ is uniquely determined by the central values of the Rankin-Selberg $L$-functions $L(\mathbf{f}\otimes\mathbf{g}, \frac{1}{2})$, where $\mathbf{f}$ runs through all primitive Hilbert cusp forms of weight $k$ for infinitely many weight vectors $k$. This work is a generalization of a result of Ganguly, Hoffstein, and Sengupta to the setting of totally real number fields, and it is a weight aspect analogue of the authors recent work.

math.NT↗

arXiv2016

Ternary Quadratic Forms And Half-Integral Weight Modular Forms

Let $k$ be a positive integer such that $k\equiv3\mod4$, and let $N$ be a positive square-free integer. In this paper, we compute a basis for the two-dimensional subspace $S_{\frac{k}{2}}(Γ_{0}(4N),F)$ of half-integral weight modular forms associated, via the Shimura correspondence, to a newform $F\in S_{k-1}(Γ_{0}(N))$, which satisfies $L(F,\frac{1}{2})\neq0$. This is accomplished by using a result of Waldspurger, which allows one to produce a basis for the forms that correspond to a given $F$ via local considerations, once a form in the Kohnen space has been determined

math.NT↗

arXiv2016

Special Values of Anticyclotomic L-functions Modulo λ

The purpose of this article is to generalize some results of Vatsal on studying the special values of Rankin-Selberg L-functions in an anticyclotomic $\mathbb{Z}_{p}$-extension. Let $g$ be a cuspidal Hilbert modular form of parallel weight (2,...,2) and level $\mathcal{N}$ over a totally real field F, and let K/F be a totally imaginary quadratic extension of relative discriminant $\mathcal{D}$. We study the $l$-adic valuation of the special values $L(g,χ,\frac{1}{2})$ as χvaries over the ring class characters of K of $\mathcal{P}$-power conductor, for some fixed prime ideal $\mathcal{P}$. We prove our results under the only assumption that the prime to $\mathcal{P}$ part of $\mathcal{N}$ is relatively prime to $\mathcal{D}$.

math.NT↗