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math.NT2020
Distribution properties for t-hooks in partitions
William Craig, Anna Pun
Partitions, the partition function , and the hook lengths of their Ferrers-Young diagrams are important objects in combinatorics, number theory and representation theory. For…
math.NT2020★ 1 cited
Variations of Lehmer's Conjecture for Ramanujan's tau-function
Jennifer S. Balakrishnan, William Craig, Ken Ono
We consider natural variants of Lehmer's unresolved conjecture that Ramanujan's tau-function never vanishes. Namely, for we prove that $$τ(n)\not \in \{\pm 1, \pm 3, \pm 5, \…
math.NT2020
Variants of Lehmer's speculation for newforms
Jennifer S. Balakrishnan, William Craig, Ken Ono +1
In the spirit of Lehmer's unresolved speculation on the nonvanishing of Ramanujan's tau-function, it is natural to ask whether a fixed integer is a value of or is a Fourier…