Ali Hamieh

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20182023

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7 papers · 1 filter

math.NT2023

Large Sums of Fourier Coefficients of Cusp Forms

Claire Frechette, Mathilde Gerbelli-Gauthier, Alia Hamieh +1

Let $N$ be a fixed positive integer, and let $f \in S_{k} (N)$ be a primitive cusp form given by the Fourier expansion $f (z) = \sum_{n = 1}^{\infty} λ_{f} (n) n^{\frac{k - 1}{2}} e (n z)$ . We consi…

math.NT2023

Quartic Gauss sums over primes and metaplectic theta functions

Chantal David, Alexander Dunn, Alia Hamieh +1

We improve 1987 estimates of Patterson for sums of quartic Gauss sums over primes. Our Type-I and Type-II estimates feature new ideas, including use of the quadratic large sieve ov…

math.NT2022

The Distribution of Values of $\frac{L ^{'}}{L} (1/2 + ε, χ_{D})$

Alia Hamieh, Rory McClenagan

We determine the limiting distribution of the family of values $\frac{L ^{'}}{L} (1/2 + ε, χ_{D})$ as $D$ varies over fundamental discriminants. Here, $0 < ε < \frac{1}{2}$ , and $χ_{D}$ is the real ch…

math.NT2021

Two dimensional value-distribution of cubic Hecke $L$ -functions

Amir Akbary, Alia Hamieh

We establish the two-dimensional asymptotic distributions of the logarithm and logarithmic derivative of $L$ -functions associated with a family of cubic Hecke characters. A crucial…

math.NT2020

Non-Vanishing of Derivatives of L-Functions of Hilbert Modular Forms in The Critical Strip

Alia Hamieh, Wissam Raji

In this paper, we show that, on average, the derivatives of $L$ -functions of cuspidal Hilbert modular forms with sufficiently large weight $k$ do not vanish on the line segments $\…

math.NT2018

Non-vanishing of Rankin-Selberg Convolutions for Hilbert Modular Form

Alia Hamieh, Naomi Tanabe

In this paper, we study the non-vanishing of the central values of the Rankin-Selberg $L$ -function of two adèlic Hilbert primitive forms $f$ and $g$ , both of which have…