B. Doyle

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20172026

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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…

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

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

Subconvexity of Short $k$ -Free Exponential Sums