Anji Dong

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math.NT2026

On a Conjecture about Sums Involving Farey Fractions

Anji Dong, Xinyi Li, Vi Anh Nguyen

In this paper, we prove a conjecture by Daniele Mundici on the sum of squared distances between consecutive elements in the $Q$ -th Farey sequence for $Q \in Z$ and $Q \geq 2$ …

math.NT2026

Bilinear forms with Kloosterman fractions and applications

Anji Dong, Nicolas Robles, Dirk Zeindler

We establish improved bounds for bilinear forms with Kloosterman fractions of the form $\sum\sum_{m, n} α_{m} β_{n} e (a m / (bn))$ with $M < m \leq 2 M$ , $N < n \leq 2 N$ and $(m,n)=…

math.NT2024

Exponential sums twisted by general arithmetic functions

Anji Dong, Nicolas Robles, Alexandru Zaharescu +1

We examine exponential sums of the form $\sum_{n \leq X} w (n) e^{2 π i α n^{k}}$ , for $k = 1, 2$ , where $α$ satisfies a generalized Diophantine approximation and where $w$ are different arit…

math.NT2024

On the order of 4-dimensional regular polytope numbers

Anji Dong, The Nguyen, Alexandru Zaharescu

In light of Kim's conjecture on regular polytopes of dimension four, which is a generalization of Waring's problem, we establish asymptotic formulas for representing any sufficient…

math.NT2024

Strange and pseudo-differentiable functions with applications to prime partitions

Anji Dong, Nicolas Robles, Alexandru Zaharescu +1

Let $p_{P_{r}} (n)$ denote the number of partitions of $n$ into $r$ -full primes. We use the Hardy-Littlewood circle method to find the asymptotic of $\mathfrak{p}_…

math.NT2024

An Equidistribution Result for Differences Associated with Square Pyramidal Numbers

Anji Dong, Katerina Saettone, Kendra Song +1

We provide an asymptotic formula for the average value of the sequence A351830: $a_{n} = ∣ P_{n} - y_{n}^{2} ∣$ for $1 \leq n \leq x$ , where $P_{n}$ is the $n$ -th square pyramidal nu…