Nickolas Andersen

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20162022

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math.NT2022

Hybrid subconvexity and the partition function

Nickolas Andersen, Han Wu

We give an upper bound for the error term in the Hardy-Ramanujan-Rademacher formula for the partition function. The main input is a new hybrid subconvexity bound for the central va…

math.NT2022

The Kohnen-Zagier formula for Maass forms for $Γ_{0} (4)$

Nickolas Andersen

We extend a formula of Duke, Imamōglu, and Tóth (which itself is a generalization of the Katok-Sarnak formula) to prove the Kohnen-Zagier formula for Maass forms for $Γ_{0} (4)$ .

math.NT2021

Non-convex geometry of numbers and continued fractions

Nickolas Andersen, William Duke, Zach Hacking +1

In recent work, the first two authors constructed a generalized continued fraction called the $p$ -continued fraction, characterized by the property that its convergents (a subseque…

math.NT2020

Zeros of $GL_{2}$ $L$ -functions on the critical line

Nickolas Andersen, Jesse Thorner

We use Levinson's method and the work of Blomer and Harcos on the $GL_{2}$ shifted convolution problem to prove that at least 6.96% of the zeros of the L-function of any hol…

math.NT2019

The Minkowski chain and Diophantine approximation

Nickolas Andersen, William Duke

The Hurwitz chain gives a sequence of pairs of Farey approximations to an irrational real number. Minkowski gave a criterion for a number to be algebraic by using a certain general…

math.NT2019

On a theorem of Davenport and Schmidt