1 citations · 1 across the 15 of their papers we have counts for
16 papers
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 removed from its four corners. In particular, we establish an asymptot…
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…
Erdős-Moser Equation in Arithmetic Progressions
Anji Dong, Vi Anh Nguyen, Alexandru Zaharescu
We consider the Erdős-Moser equation in arithmetic progressions. We prove among other things that when , for any solution to exist, the above sum…
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.
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 denote the sum of squared distances between consecutive Farey fractions in the full interval . Daniele Mundici conjectured that $C(Q):=D_{2}(Q)\cdot Q^2/\log…
The Conjecture and the Riemann Hypothesis for Automorphic -functions
Anji Dong, Nawapan Wattanawanichkul, Alexandru Zaharescu
The conjecture asserts that the mollified second moments of the Riemann zeta function remain bounded for mollifiers of arbitrary polynomial length. We investigate an ana…
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 -th Farey sequence for and …
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 with , and $(m,n)=…
Zeros of Polynomials in Derivatives of Automorphic -functions
Anji Dong, Nawapan Wattanawanichkul, Alexandru Zaharescu
Let be the set of all cuspidal automorphic representations of , and let be a polynomial in the derivati…
Cannonball Polygons with Multiplicities
Anji Dong, Katerina Saettone, Kendra Song +1
We generalize the Cannonball Problem by introducing integer-valued and non-increasing arithmetic functions . We associate these functions with certain polygons, which we cal…
An Equidistribution Result for Differences Associated to Square Pyramidal Numbers II
Anji Dong, Katerina Saettone, Kendra Song +1
This paper presents some new results concerned with uniform distribution properties associated with the sequence , which is defined as the distance from the…
Exponential sums twisted by general arithmetic functions
Anji Dong, Nicolas Robles, Alexandru Zaharescu +1
We examine exponential sums of the form , for , where satisfies a generalized Diophantine approximation and where are different arit…
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…
Strange and pseudo-differentiable functions with applications to prime partitions
Anji Dong, Nicolas Robles, Alexandru Zaharescu +1
Let denote the number of partitions of into -full primes. We use the Hardy-Littlewood circle method to find the asymptotic of $\mathfrak{p}_…
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: for , where is the -th square pyramidal nu…
Almost all primes are not needed in Ternary Goldbach
Debmalya Basak, Raghavendra N. Bhat, Anji Dong +1
The ternary Goldbach conjecture states that every odd number can be written as the sum of three primes. We construct a set of primes defined by an expa…