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Cancellation in Sums of Hecke Eigenvalues Over Quadratic Polynomials and Mass Equidistribution
Steven Creech
https://arxiv.org/abs/2508.18666 https://arxiv…

Cancellation in Sums of Hecke Eigenvalues Over Quadratic Polynomials and Mass Equidistribution
We study cancellation in sums of Hecke eigenvalues over irreducible quadratic polynomials over short intervals. In particular, we look at an average over bases of Hecke forms of weight $k$ in the range $\vert k-K\vert

Products of strictly hyperbolic conjugacy classes in symplectic groups
Klaus Nielsen
https://arxiv.org/abs/2509.26237 https://arxiv.org/pdf/2509.26237

Products of strictly hyperbolic conjugacy classes in symplectic groups
We call a conjugacy class of the symplectic group Sp$(2n, K)$ over a field $K$ strictly hyperbolic if its minimal polynomial is of the form $q(x) q^*(x)$, where the polynomial $q(x)$ is prime to its reciprocal $q^*(x) := x^n q(x^{-1})$. It is shown that the product of 2 cyclic, strictly hyperbolic conjugacy classes of Sp$(2n, K)$ contains all nonscalar elements of Sp$(2n, K)$. It follows that the projective symplectic group has a conjugacy class of covering number 2, i.e. PSp$(2n,K) = Ω^2$ for…