Jonathan W. Bober

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20242026

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math.NT2026

Distribution of mixed character sums and extremal problems for Littlewood polynomials

Jonathan W. Bober, Oleksiy Klurman, Besfort Shala

We prove distributional results for mixed character sums \begin{equation*} \sum_{n\le x }Ï(n)e(nÎ¸), \end{equation*} for fixed $I^¸ \in [0, 1]$ and random character $I ¨ (mod q)$ , as w…

math.NT2025

Murmurations of modular forms in the weight aspect

Jonathan Bober, Andrew R. Booker, Min Lee +1

We prove the existence of "murmurations" in the family of holomorphic modular forms of level $1$ and weight $k \to \infty$ , that is, correlations between their root numbers and Hecke…

math.NT2024

On $2$ -superirreducible polynomials over finite fields

Jonathan W. Bober, Lara Du, Dan Fretwell +2

We investigate $k$ -superirreducible polynomials, by which we mean irreducible polynomials that remain irreducible under any polynomial substitution of positive degree at most $k$ .…

math.NT2024

A converse to a theorem of Gauss on Gauss sums

Jonathan W. Bober, Leo Goldmakher

In this note we prove (under mild hypotheses) that $f$ is a nontrivial character of $F_{p}$ if and only if the Fourier transform of $f$ has magnitude 1 somewhere in $\mathbb…

Distribution of mixed character sums and extremal problems for Littlewood polynomials

Murmurations of modular forms in the weight aspect

On 2-superirreducible polynomials over finite fields

A converse to a theorem of Gauss on Gauss sums

On $2$ -superirreducible polynomials over finite fields