117 citations · 229 across the 18 of their papers we have counts for
20 papers
Distributions of Hook lengths in integer partitions
Michael Griffin, Ken Ono, Wei-Lun Tsai
Motivated by the many roles that hook lengths play in mathematics, we study the distribution of the number of -hooks in the partitions of . We prove that the limiting distrib…
Limiting Betti distributions of Hilbert schemes on points
Michael Griffin, Ken Ono, Larry Rolen +1
Hausel and Rodriguez-Villegas recently observed that work of Göttsche, combined with a classical result of Erdős and Lehner on integer partitions, implies that the limiting Betti d…
AGM and jellyfish swarms of elliptic curves
Michael J. Griffin, Ken Ono, Neelam Saikia +1
The classical produces wonderful interdependent infinite sequences of arithmetic and geometric means with common limit. For finite fields with $q\equ…
Tamagawa products of elliptic curves over
Michael Griffin, Ken Ono, Wei-Lun Tsai
We explicitly construct the Dirichlet series where is the proportion of elliptic…
The arithmetic of modular grids
Michael Griffin, Paul Jenkins, Grant Molnar
A modular grid is a pair of sequences and of weakly holomorphic modular forms such that for almost all and , the coefficient of in is the neg…
Heights of points on elliptic curves over
Michael Griffin, Ken Ono, Wei-Lun Tsai
In this note we obtain effective lower bounds for the canonical heights of non-torsion points on by making use of suitable elliptic curve ideal class pairings $$Ψ_{…
Quadratic twists of elliptic curves and class numbers
Michael Griffin, Ken Ono, Wei-Lun Tsai
For positive rank elliptic curves , we employ ideal class pairings for quadratic twists…
Divisors of Modular Parametrizations of Elliptic Curves
Michael Griffin, Jonathan Hales
The modularity theorem implies that for every elliptic curve there exist rational maps from the modular curve to , where is the conductor of . Th…
Elliptic curves and lower bounds for class numbers
Michael Griffin, Ken Ono
Ideal class pairings map the rational points of rank elliptic curves $E/\Q$ to the ideal class groups $\CL(-D)$ of certain imaginary quadratic fields. These pairings impl…
Jensen Polynomials for the Riemann Xi Function
Michael Griffin, Ken Ono, Larry Rolen +3
We investigate Riemann's xi function (here is the Riemann zeta function). The Riemann Hypothesis (RH) asserts tha…
Jensen polynomials for the Riemann zeta function and other sequences
Michael Griffin, Ken Ono, Larry Rolen +1
In 1927 Pólya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for the Riemann zeta function at its point of symmetry. This hyperb…
When are Multiples of Polygonal Numbers again Polygonal Numbers?
Jasbir S. Chahal, Michael Griffin, Nathan Priddis
Euler showed that there are infinitely many triangular numbers that are three times other triangular numbers. In general, it is an easy consequence of the Pell equation that for a…
On p-adic haromonic Maass functions
Michael J. Griffin
Modular and mock modular forms possess many striking -adic properties, as studied by Bringmann, Guerzhoy, Kane, Kent, Ono, and others. Candelori developed a geometric theory of…
A proof of the Thompson Moonshine Conjecture
Michael J. Griffin, Michael H. Mertens
In this paper we prove the existence of an infinite dimensional graded super-module for the finite sporadic Thompson group whose McKay-Thompson series are weakly holomorphic m…
On p-adic modular forms and the Bloch-Okounkov theorem
Michael Griffin, Marie Jameson, Sarah Trebat-Leder
Bloch-Okounkov studied certain functions on partitions called shifted symmetric polynomials. They showed that certain -series arising from these functions (the so-called \em…
Proof of the Umbral Moonshine Conjecture
John F. R. Duncan, Michael J. Griffin, Ken Ono
The Umbral Moonshine Conjectures assert that there are infinite-dimensional graded modules, for prescribed finite groups, whose McKay-Thompson series are certain distinguished mock…
Moonshine
John F. R. Duncan, Michael J. Griffin, Ken Ono
Monstrous moonshine relates distinguished modular functions to the representation theory of the monster. The celebrated observations that 196884=1+196883 and 21493760=1+196883+2129…
Weierstrass mock modular forms and elliptic curves
Claudia Alfes, Michael Griffin, Ken Ono +1
Mock modular forms, which give the theoretical framework for Ramanujan's enigmatic mock theta functions, play many roles in mathematics. We study their role in the context of modul…
A framework of Rogers-Ramanujan identities and their arithmetic properties
Michael J. Griffin, Ken Ono, S. Ole Warnaar
The two Rogers-Ramanujan -series \[ \sum_{n=0}^{\infty}\frac{q^{n(n+σ)}}{(1-q)\cdots (1-q^n)}, \] where , play many roles in mathematics and physics. By the Rogers-Ramanu…
SU(2)-Donaldson invariants of the complex projective plane
Michael Griffin, Andreas Malmendier, Ken Ono
There are two families of Donaldson invariants for the complex projective plane, corresponding to the SU(2)-gauge theory and the SO(3)-gauge theory with non-trivial Stiefel-Whitney…