Anne Larsen

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20192026

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math.NT2021

Some Remarks on Small Values of $τ (n)$

Kaya Lakein, Anne Larsen

A natural variant of Lehmer's conjecture that the Ramanujan $τ$ -function never vanishes asks whether, for any given integer $α$ , there exist any $n \in Z^{+}$ such that $τ(n…

math.NT2021

A Proof of Merca's Conjectures on Sums of Odd Divisor Functions

Kaya Lakein, Anne Larsen

In a recent paper, Merca posed three conjectures on congruences for specific convolutions of a sum of odd divisor functions with a generating function for generalized $m$ -gonal num…

math.NT2021

Supersingular Loci from Traces of Hecke Operators

Kevin Gomez, Kaya Lakein, Anne Larsen

A classical observation of Deligne shows that, for any prime $p \geq 5$ , the divisor polynomial of the Eisenstein series $E_{p - 1} (z)$ mod $p$ is closely related to the supersingula…

math.NT2019

Multiplicative Series, Modular Forms, and Mandelbrot Polynomials

Michael Larsen

We say a power series $\sum_{n = 0}^{\infty} a_{n} q^{n}$ is multiplicative if the function $n \mapsto a_{n} / a_{1}$ ( $n \geq 1$ ) is so. In this paper, we consider multiplicative power series $f$ …

Some Remarks on Small Values of τ(n)

A Proof of Merca's Conjectures on Sums of Odd Divisor Functions

Supersingular Loci from Traces of Hecke Operators

Multiplicative Series, Modular Forms, and Mandelbrot Polynomials

Some Remarks on Small Values of $τ (n)$