C. Kuan

activity

20112025

most citedSecond Moments in the Generalized Gauss Circle Problem

21 citations · 53 across the 15 of their papers we have counts for

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20 papers · 1 filter

math.NT2025

Murmurations using Petersson trace formula

Chan Ieong Kuan, Didier Lesesvre

We prove the murmuration phenomenon, which is a correlation between signs of functional equations and Fourier coefficients, in the case of modular forms in the weight aspect. We in…

math.NT2025

On the Asymptotic Density of $k$ -tuples of Positive Integers Satisfying Arbitrary GCD Conditions

Chan Ieong Kuan

We consider the problem of counting $k$ -tuples of positive integers satisfying any arbitrary set of gcd conditions, where every integer is not larger than $x$ . We first establish t…

math.NT2025

The Fibonacci Zeta Function and Modular Forms

Eran Assaf, Chan Ieong Kuan, David Lowry-Duda +1

We show that a family of Dirichlet series generalizing the Fibonacci zeta function $\sum F (n)^{- s}$ has meromorphic continuation in terms of dihedral $GL (2)$ Maass forms.

math.NT2024

The Fibonacci Zeta Function and Continuation

Eran Assaf, Chan Ieong Kuan, David Lowry-Duda +1

We introduce a family of Dirichlet series associated to real quadratic number fields that generalize the ordinary Fibonacci zeta function $\sum F (n)^{- s}$ , where $F (n)$ denotes the…

math.NT2023

Counting Divisors in the Outputs of a Binary Quadratic Form

Chan Ieong Kuan, David Lowry-Duda, Alexander Walker +1

For a fixed natural number $h$ , we prove meromorphic continuation of the two-variable Dirichlet series $\sum_{m} r_{2} (m) σ_{w} (m + h) (m + h)^{- s + w}$ to $C^{2}$ and use this to…

math.NT2023

Sums of Cusp Form Coefficients Along Quadratic Sequences

Chan Ieong Kuan, David Lowry-Duda, Alexander Walker +1

Let $f (z) = \sum A (n) n^{(k - 1) /2} e (n z)$ be a cusp form of weight $k \geq 3$ on $Γ_{0} (N)$ with character $χ$ . By studying a certain shifted convolution sum, we prove that $\sum_{n \…

math.NT2021

Subconvexity for twisted GL(3) L-functions

Eren Mehmet Kıral, Chan Ieong Kuan, Didier Lesesvre

Using the circle method, we obtain subconvex bounds for GL(3) L-functions twisted by a character modulo a prime p, hybrid in the t and p-aspects.

math.NT2020

Arithmetic Progressions of Squares and Multiple Dirichlet Series

Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1

We study a Dirichlet series in two variables which counts primitive three-term arithmetic progressions of squares. We show that this multiple Dirichlet series has meromorphic conti…

math.NT2020

Quadratic twists of central values for GL(3)

Chan Ieong Kuan, Didier Lesesvre

We prove that a cuspidal automorphic representation of GL(3) over any number field is determined by the quadratic twists of its central value. In the case of a non-Gelbart-Jacquet…

math.NT2020★ 2 cited

Sums of even ascending powers

Chan Ieong Kuan, Didier Lesesvre, Xuanxuan Xiao

Freiman and Scourfield proved that any large enough integer can be written as a sum of a certain number of ascending even powers. We use the circle method to provide the first expl…

math.NT2019★ 6 cited

Triple Correlation Sums of Coefficients of Cusp Forms

Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1

We produce nontrivial asymptotic estimates for shifted sums of the form $\sum a (h) b (m) c (2 m - h)$ , in which $a (n), b (n), c (n)$ are un-normalized Fourier coefficients of holomorphic cusp…

math.NT2018★ 4 cited

A Shifted Sum for the Congruent Number Problem

Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1

We introduce a shifted convolution sum that is parametrized by the squarefree natural number $t$ . The asymptotic growth of this series depends explicitly on whether or not $t$ is a…

math.NT2017★ 4 cited

The Laplace Transform of the Second Moment in the Gauss Circle Problem

Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1

The Gauss circle problem concerns the difference $P_{2} (n)$ between the area of a circle of radius $n$ and the number of lattice points it contains. In this paper, we study th…

math.NT2017★ 21 cited

Second Moments in the Generalized Gauss Circle Problem

Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1

The generalized Gauss circle problem concerns the lattice point discrepancy of large spheres. We study the Dirichlet series associated to $P_{k} (n)^{2}$ , where $P_{k} (n)$ is the discrepa…

math.NT2016★ 6 cited

Sign Changes of Coefficients and Sums of Coefficients of L-Functions

Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1

We extend the axiomatization for detecting and quantifying sign changes of Meher and Murty to sequences of complex numbers. We further generalize this result when the sequence is c…

math.NT2015★ 3 cited

Short-Interval Averages of Sums of Fourier Coefficients of Cusp Forms

Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1

Let $f$ be a weight $k$ holomorphic cusp form of level one, and let $S_{f} (n)$ denote the sum of the first $n$ Fourier coefficients of $f$ . In analogy with Dirichlet's divisor proble…

math.NT2015★ 7 cited

The Second Moment of Sums of Coefficients of Cusp Forms

Thomas A. Hulse, Chan Ieong Kuan, David Lowry-Duda +1

Let $f$ and $g$ be weight $k$ holomorphic cusp forms and let $S_{f} (n)$ and $S_{g} (n)$ denote the sums of their first $n$ Fourier coefficients. Hafner and Ivic [HI], building on Chandr…

math.NT2013

Hybrid Bounds on Twisted L-Functions Associated to Modular Forms

Chan Ieong Kuan

For $f$ a primitive holomorphic cusp form of even weight $k \geq 4$ , level $N$ , and $χ$ a Dirichlet character mod $Q$ with $(Q, N) = 1$ , we establish a new hybrid subconvexity bound f…

math.NT2013

Counting Square Discriminants

Thomas A. Hulse, E. Mehmet Kıral, Chan Ieong Kuan +1

Counting integral binary quadratic forms with certain restrictions is a classical problem. In this paper, we count binary quadratic forms of fixed discriminant given restrictions o…

math.NT2011

The Sign of Fourier Coefficients of Half-Integral Weight Cusp Forms

Thomas A. Hulse, E. Mehmet Kiral, Chan Ieong Kuan +1

From a result of Waldspurger, it is known that the normalized Fourier coefficients $a (m)$ of a half-integral weight holomorphic cusp eigenform $\f$ are, up to a finite set of facto…

Murmurations using Petersson trace formula

On the Asymptotic Density of k-tuples of Positive Integers Satisfying Arbitrary GCD Conditions

The Fibonacci Zeta Function and Modular Forms

The Fibonacci Zeta Function and Continuation

Counting Divisors in the Outputs of a Binary Quadratic Form

Sums of Cusp Form Coefficients Along Quadratic Sequences

Subconvexity for twisted GL(3) L-functions

Arithmetic Progressions of Squares and Multiple Dirichlet Series

Quadratic twists of central values for GL(3)

Sums of even ascending powers

Triple Correlation Sums of Coefficients of Cusp Forms

A Shifted Sum for the Congruent Number Problem

The Laplace Transform of the Second Moment in the Gauss Circle Problem

Second Moments in the Generalized Gauss Circle Problem

Sign Changes of Coefficients and Sums of Coefficients of L-Functions

Short-Interval Averages of Sums of Fourier Coefficients of Cusp Forms

The Second Moment of Sums of Coefficients of Cusp Forms

Hybrid Bounds on Twisted L-Functions Associated to Modular Forms

Counting Square Discriminants

The Sign of Fourier Coefficients of Half-Integral Weight Cusp Forms

On the Asymptotic Density of $k$ -tuples of Positive Integers Satisfying Arbitrary GCD Conditions