arXiv subjects

Archer Clayton

Publications and source records attributed to Archer Clayton.

2 recordsLinked to original sources

arXiv2025

Non-repetition of second coefficients of Hecke polynomials

Let $T_m(N,2k)$ denote the $m$-th Hecke operator on the space $S_{2k}(Γ_0(N))$ of cuspidal modular forms of weight $2k$ and level $N$. In this paper, we study the non-repetition of the second coefficient of the characteristic polynomial of $T_m(N,2k)$. We obtain results in the horizontal aspect (where $m$ varies), the vertical aspect (where $k$ varies), and the level aspect (where $N$ varies). Finally, we use these non-repetition results to extend a result of Vilardi and Xue on distinguishing Hecke eigenforms.

math.NT↗

arXiv2024

The effect of the trace operator on the duality of modular grids in genus zero levels

Griffin, the second author, and Molnar studied coefficient duality for canonical bases for a broad range of spaces of weakly holomorphic modular forms, showing that the Fourier coefficients of canonical basis elements appear as negatives of Fourier coefficients for elements of a canonical basis of a related space of forms. We investigate the effect of the trace operator on this duality for modular forms for $Γ_0(N)$ of genus zero and show exactly when duality still holds after applying the trace operator.

math.NT↗