David T. Nguyen

most citedGeneralized divisor functions in arithmetic progressions: I

5 citations · 5 across the 3 of their papers we have counts for

collaborators

3 papers

math.NT2023

A translation of N.M. Katz's "Exponential Sums"

David T. Nguyen

These notes are devoted to the theory of exponential sums over finite fields. The first chapter recalls some of the number-theoretic interest of such sums. The second chapter discu…

math.NT2023★ 5 cited

Generalized divisor functions in arithmetic progressions: I

David T. Nguyen

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 con…

math.NT2023

On Ramanujan-Fourier expansions

David T. Nguyen

We heuristically study the shifted convolution $\sum_{n \leq X} τ_{k} (n) τ_{ℓ} (n + h)$ using a normalized version of Ramanujan-Fourier expansions for $τ_{k} (n)$ and verify they produce th…