Alexandru Zaharescu

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20242026

most citedRepresentations as Sums of Icosahedral and Dodecahedral Numbers: Proof of Pollock's Conjectures

1 citations · 1 across the 18 of their papers we have counts for

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math.NT2026

Simultaneous Unimodularity of Positive Integer Matrices and Their Entrywise Cubes

Xinyi Li, Shuochen Wang, Zimeng Ye +1

We solve an open problem posed by Richard Guy in his book Unsolved Problems in Number Theory. We prove that, for every integer $n \geq 10$ , there exist infinitely many $n \times n$ in…

math.NT2026

On the exponential sum over squarefree integers

Nicolas Robles, Alexandru Zaharescu, Dirk Zeindler

Let $μ$ be the Möbius function and $e (t) = e^{2 π i t}$ . We prove that if $N \geq 2$ , $α \in R$ , $(a, q) = 1$ , and $∣ α - a / q ∣ \leq q^{- 2}$ , then \[\bigg|\sum_{n\le N}μ^2(n)e(αn)\bigg|\ll\l…

math.NT2026

Self-intersection Points of Billiard Trajectories in a Square with Small Pockets

Anji Dong, Colin Edsey, Shuta Iwai +1

We study the self-intersections of billiard trajectories in a square with small pockets of size $ε$ removed from its four corners. In particular, we establish an asymptot…

math.NT2026★ 1 cited

Representations as Sums of Icosahedral and Dodecahedral Numbers: Proof of Pollock's Conjectures

Debmalya Basak, Anji Dong, Katerina Saettone +1

On the occasion of George Andrews' and Bruce Berndt's combined 170th birthday, we prove two conjectures of Sir Frederick Pollock that are more than 170 years old. In 1843, Pollock…

math.NT2026

Erdős-Moser Equation in Arithmetic Progressions

Anji Dong, Vi Anh Nguyen, Alexandru Zaharescu

We consider the Erdős-Moser equation $1^{k} + 2^{k} + \dots + (m - 1)^{k} = m^{k}$ in arithmetic progressions. We prove among other things that when $k = 2$ , for any solution to exist, the above sum…

math.NT2026

Admissible Pairs: A Variation to Pollock Conjectures

Anji Dong, Vi Anh Nguyen, Alexandru Zaharescu

We introduce a notion of an admissible pair, and prove a variation to Pollock's conjectures on icosahedral and dodecahedral numbers.

math.NT2026

Binomial coefficients with divisors avoiding an interval

Hung M. Bui, Slava Naprienko, Kyle Pratt +1

We solve a fifty-year-old conjecture of Erdős and Graham concerning whether the binomial coefficient $(k n)$ with $1 \leq k \leq \frac{n}{2}$ must always have a divisor $\le…

math.NT2026

Effective Estimates for a Class of Farey Fraction Sums and Bounds for Mundici-Type Constants

Anji Dong, Huy Xuan Nguyen, Vi Anh Nguyen +1

Let $D_{2} (Q)$ denote the sum of squared distances between consecutive Farey fractions in the full interval $(0, 1]$ . Daniele Mundici conjectured that $C(Q):=D_{2}(Q)\cdot Q^2/\log…

math.NT2026

The $θ = \infty$ Conjecture and the Riemann Hypothesis for Automorphic $L$ -functions

Anji Dong, Nawapan Wattanawanichkul, Alexandru Zaharescu

The $θ = \infty$ conjecture asserts that the mollified second moments of the Riemann zeta function remain bounded for mollifiers of arbitrary polynomial length. We investigate an ana…

math.NT2026

A statistical model for points expanding in higher dimensions while being tied to bijective involutions

Cristian Cobeli, The Nguyen, Alexandru Zaharescu

Let $M$ be a set with $M$ elements, let $ψ : M \to M$ be a bijective involution, and let~ $X_{ψ}$ be the set of sequences $(x_1,\dots,…

Simultaneous Unimodularity of Positive Integer Matrices and Their Entrywise Cubes

On the exponential sum over squarefree integers

Self-intersection Points of Billiard Trajectories in a Square with Small Pockets

Representations as Sums of Icosahedral and Dodecahedral Numbers: Proof of Pollock's Conjectures

Erdős-Moser Equation in Arithmetic Progressions

Admissible Pairs: A Variation to Pollock Conjectures

Binomial coefficients with divisors avoiding an interval

Effective Estimates for a Class of Farey Fraction Sums and Bounds for Mundici-Type Constants

The θ=∞ Conjecture and the Riemann Hypothesis for Automorphic L-functions

A statistical model for points expanding in higher dimensions while being tied to bijective involutions

The $θ = \infty$ Conjecture and the Riemann Hypothesis for Automorphic $L$ -functions