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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…
On the Pair Correlation of Zeros of -Functions for Non-CM Newforms in Shifted Ranges
Di Liu, Clayton Williams, Alexandru Zaharescu
We study the pair correlation between zeros of a shifted auxiliary -function attached to a non-CM newform, the scale of which is a fixed constant. We prove an unconditional as…
Euler Product Sieve
Di Liu, Yuri Matiyasevich, Joseph Oesterlé +1
We study a class of approximations to the Riemann zeta function introduced earlier by the second author on the basis of Euler product. This allows us to justify Euler Product Sieve…