Nate Gillman

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20182026

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math.NT2019

Patterns of primes in the Sato-Tate conjecture

Nate Gillman, Michael Kural, Alexandru Pascadi +2

Fix a non-CM elliptic curve $E / Q$ , and let $a_{E} (p) = p + 1 - # E (F_{p})$ denote the trace of Frobenius at $p$ . The Sato-Tate conjecture gives the limiting distribut…

math.NT2019

Explicit subconvexity savings for sup-norms of cusp forms on $PGL_{n} (R)$

Nate Gillman

Blomer and Maga recently proved that, if $F$ is an $L^{2}$ -normalized Hecke Maass cusp form for $SL_{n} (Z)$ , and $Ω$ is a compact subset of $\mathrm{PGL}_n(\mathbb R)/…

math.NT2019

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…

math.NT2018

Exact Formulas for Invariants of Hilbert Schemes

Nate Gillman, Xavier Gonzalez, Matthew Schoenbauer

A theorem of Göttsche establishes a connection between cohomological invariants of a complex projective surface $S$ and corresponding invariants of the Hilbert scheme of $n$ points…

Patterns of primes in the Sato-Tate conjecture

Explicit subconvexity savings for sup-norms of cusp forms on PGLn​(R)

From partitions to Hodge numbers of Hilbert Schemes of Surfaces

Exact Formulas for Invariants of Hilbert Schemes

Explicit subconvexity savings for sup-norms of cusp forms on $PGL_{n} (R)$