B. Doyle

activity

20172026

collaborators

5 papers

math.NT2026

Subconvexity of Short $k$ -Free Exponential Sums in $F_{q} [t]$

Ben Doyle

We extend recent work of the author over $Z$ into the positive characteristic setting of $F_{q} [t]$ . In particular, for a polynomial $F \in F_{q} [t]$ of degr…

math.NT2026

Subconvexity of Short $k$ -Free Exponential Sums

Ben Doyle

Let $S_{k} (α; K)$ denote the exponential sum over $k$ -free integers in the short interval $(N - K, N]$ . For $s > 0$ , we prove essentially tight bounds on the $s$ -th moments of $S_{k} (α; K)$ w…

math.NT2025

On the Moments of Exponential Sums over r-Free Polynomials

Ben Doyle

Let $F_{q} [t]$ denote the ring of polynomials over the finite field $F_{q}$ . Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we dete…

math.CO2023

Algorithms for Chip-Firing on Weighted Graphs

Ben Doyle

We extend the notion of chip-firing to weighted graphs, and generalize the Greedy Algorithm and Dhar's Burning Algorithm to weighted graphs. For a vertex $q \in V (Γ)$ , we give an u…

cs.CR2017

Trustware: A Device-based Protocol for Verifying Client Legitimacy

Ben Doyle, Patrick Korth, Kyle Nekritz +1

Online services commonly attempt to verify the legitimacy of users with CAPTCHAs. However, CAPTCHAs are annoying for users, often difficult for users to solve, and can be defeated…

Subconvexity of Short k-Free Exponential Sums in Fq​[t]

Subconvexity of Short k-Free Exponential Sums

On the Moments of Exponential Sums over r-Free Polynomials

Algorithms for Chip-Firing on Weighted Graphs

Trustware: A Device-based Protocol for Verifying Client Legitimacy

Subconvexity of Short $k$ -Free Exponential Sums in $F_{q} [t]$

Subconvexity of Short $k$ -Free Exponential Sums