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21 papers · 1 filter
Computations directly on the cuspidal cohomology of congruence subgroups of
Zachary Porat
Ash, Grayson, and Green [J. Number Theory 19 (1984), pp. 412-436] compute the action of Hecke operators on a certain subspace of the cohomology of low-level congruence subgroups of…
Bilateral series and Ramanujan's radial limits
Jitendra Bajpai, Susie Kimport, Jie Liang +2
Ramanujan's last letter to Hardy explored the asymptotic properties of modular forms, as well as those of certain interesting -series which he called \emph{mock theta functions}…
Abundance of Dirichlet-improvable pairs with respect to arbitrary norms
Dmitry Kleinbock, Anurag Rao
In a recent paper of Akhunzhanov and Shatskov the two-dimensional Dirichlet spectrum with respect to Euclidean norm was defined. We consider an analogous definition for arbitrary n…
Patterns of primes in the Sato-Tate conjecture
Nate Gillman, Michael Kural, Alexandru Pascadi +2
Fix a non-CM elliptic curve , and let denote the trace of Frobenius at . The Sato-Tate conjecture gives the limiting distribut…
Explicit subconvexity savings for sup-norms of cusp forms on
Nate Gillman
Blomer and Maga recently proved that, if is an -normalized Hecke Maass cusp form for , and is a compact subset of $\mathrm{PGL}_n(\mathbb R)/…
From partitions to Hodge numbers of Hilbert Schemes of Surfaces
Nate Gillman, Xavier Gonzalez, Ken Ono +2
We celebrate the 100th anniversary of Srinivasa Ramanujan's election as a Fellow of the Royal Society, which was largely based on his work with G. H. Hardy on the asymptotic proper…