Naomi Tanabe

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20112024

most citedNotes on the arithmetic of Hilbert modular forms

33 citations · 40 across the 7 of their papers we have counts for

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math.NT2024

A Note on Large Sums of Divisor-Bounded Multiplicative Functions

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

Given a multiplicative function $f$ , we let $S (x, f) = \sum_{n \leq x} f (n)$ be the associated partial sum. In this note, we show that lower bounds on partial sums of divisor-bounded fu…

math.NT2023

An Alternative Approach to Computing $β (2 k + 1)$

Naomi Tanabe, Nawapan Wattanawanichkul

This paper presents a new approach to evaluating the special values of the Dirichlet beta function, $β (2 k + 1)$ , where $k$ is any nonnegative integer. Our approach relies on some pro…

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.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…

math.NT2017★ 7 cited

Equidistribution of signs for Hilbert modular forms of half-integral weight

Surjeet Kaushik, Narasimha Kumar, Naomi Tanabe

We prove an equidistribution of signs for the Fourier coefficients of Hilbert modular forms of half-integral weight. Our study focuses on certain subfamilies of coefficients that a…

math.NT2016

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