David T. Nguyen

David T. Nguyen
American Institute of Mathematics | AIMATH

Ph.D.

About

5
Publications
211
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22
Citations
Citations since 2017
4 Research Items
20 Citations
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20172018201920202021202220230123456
20172018201920202021202220230123456
Introduction
Skills and Expertise

Publications

Publications (5)
Preprint
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Let $\zeta^k(s) = \sum_{n=1}^\infty \tau_k(n) n^{-s}, \Re s > 1$. We present three conditional results on the additive correlation sum $$\sum_{n\le X} \tau_3(n) \tau_3(n+h)$$ and give numerical verifications of our method. The first is a conditional proof for the full main term of this correlation sum for the case $h=1$, on assuming an averaged lev...
Preprint
Full-text available
In this paper, we confirm a smoothed version of a recent conjecture on the variance of the k-fold divisor function in arithmetic progressions to individual composite moduli, in a restricted range. In contrast to a previous result of Rodgers and Soundararajan, we do not require averaging over the moduli. Our proof adapts a technique of S. Lester who...
Article
We prove some distribution results for the k-fold divisor function in arithmetic progressions to moduli that exceed the square-root of length X of the sum, with appropriate constrains and averaging on the moduli, saving a power of X from the trivial bound. On assuming the Generalized Riemann Hypothesis, we obtain uniform power saving error terms th...
Chapter
This article deals with the enumeration of directed lattice walks on the integers with any finite set of steps, starting at a given altitude j and ending at a given altitude k, with additional constraints, for example, to never attain altitude 0 in-between. We first discuss the case of walks on the integers with steps \(-h, \dots , -1, +1, \dots ,...
Article
This article deals with the enumeration of directed lattice walks on the integers with any finite set of steps, starting at a given altitude $j$ and ending at a given altitude $k$, with additional constraints such as, for example, to never attain altitude $0$ in-between. We first discuss the case of walks on the integers with steps $-h, \dots, -1,...

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