42 citations · 140 across the 19 of their papers we have counts for
16 papers · 1 filter
Bounds for the number of cohomological automorphic representations of in the weight aspect
Simon Marshall
We prove a power saving over the trivial bound for the number of cohomological cuspidal automorphic representations of fixed level and growing weight on , by adapt…
Asymptotic trace formula for the Hecke operators
Junehyuk Jung, Simon Marshall, Naser T. Sardari
Given integers , and , we give an explicit formula with an optimal error term (with square root cancelation) for the Petersson trace formula involving the -th and -…
Endoscopy and cohomology of U(n,1)
Simon Marshall, Sug Woo Shin
By assuming the endoscopic classification of automorphic representations on inner forms of unitary groups, which is currently work in progress by Kaletha, Minguez, Shin, and White,…
Lower bounds for Maass forms on semisimple groups
Farrell Brumley, Simon Marshall
Let be an anisotropic semisimple group over a totally real number field . Suppose that is compact at all but one infinite place . In addition, suppose that $G_{v_0}…
Local bounds for norms of Maass forms in the level aspect
Simon Marshall
We apply techniques from harmonic analysis to study the norms of Maass forms of varying level on a quaternion division algebra. Our first result gives a candidate for the loc…
Endoscopy and cohomology of a quasi-split U(4)
Simon Marshall
We prove asymptotic upper bounds for the Betti numbers of the locally symmetric spaces associated to a quasi-split . These manifolds are 8-dimensional, and we prove bou…