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## Algebraic and transcendental formulas for the smallest parts function

- S. Ahlgren, Nickolas Andersen
- Mathematics
- 9 April 2015

## Kloosterman sums and Maass cusp forms of half integral weight for the modular group

- S. Ahlgren, Nickolas Andersen
- Mathematics
- 18 October 2015

We estimate the sums \[ \sum_{c\leq x} \frac{S(m,n,c,\chi)}{c}, \] where the $S(m,n,c,\chi)$ are Kloosterman sums of half-integral weight on the modular group. Our estimates are uniform in $m$, $n$,… Expand

## Divisibility Properties of Coefficients of Level $p$ Modular Functions for Genus Zero Primes

- Nickolas Andersen, P. Jenkins
- Mathematics
- 6 June 2011

Lehner's 1949 results on the $j$-invariant showed high divisibility of the function's coefficients by the primes $p\in\{2,3,5,7\}$. Expanding his results, we examine a canonical basis for the space… Expand

## LEVEL RECIPROCITY IN THE TWISTED SECOND MOMENT OF RANKIN–SELBERG $L$ -FUNCTIONS

- Nickolas Andersen, E. M. Kıral
- Mathematics
- 18 January 2018

We prove an exact formula for the second moment of Rankin–Selberg $L$
-functions $L(\frac{1}{2},f\times g)$
twisted by $\unicode[STIX]{x1D706}_{f}(p)$
, where $g$
is a fixed holomorphic cusp form… Expand

## Modular invariants for real quadratic fields and Kloosterman sums

- Nickolas Andersen, W. Duke
- Mathematics
- 24 January 2018

We investigate the asymptotic distribution of integrals of the $j$-function that are associated to ideal classes in a real quadratic field. To estimate the error term in our asymptotic formula, we… Expand

## Euler-like recurrences for smallest parts functions

- S. Ahlgren, Nickolas Andersen
- Mathematics
- 21 February 2014

We obtain recurrences for smallest parts functions which resemble Euler’s recurrence for the ordinary partition function. The proofs involve the holomorphic projection of non-holomorphic modular… Expand

## Hecke-type congruences for two smallest parts functions

- Nickolas Andersen
- Mathematics
- 18 September 2012

We prove infinitely many congruences modulo 3, 5, and powers of 2 for the overpartition function $\bar{p}(n)$ and two smallest parts functions: $\bar{\operatorname{spt1}}(n)$ for overpartitions and… Expand

## Zeros of GL2 𝐿-functions on the critical line

- Nickolas Andersen, Jesse Thorner
- Mathematics
- 2 February 2021

Abstract We use Levinson’s method and the work of Blomer and Harcos on the GL2\mathrm{GL}_{2} shifted convolution problem to prove that at least 6.96 % of the nontrivial zeros of the 𝐿-function of a… Expand

## Classification of congruences for mock theta functions and weakly holomorphic modular forms

- Nickolas Andersen
- Mathematics
- 30 June 2013

Let $f(q)$ denote Ramanujan's mock theta function \[f(q) = \sum_{n=0}^{\infty} a(n) q^{n} := 1+\sum_{n=1}^{\infty} \frac{q^{n^{2}}}{(1+q)^{2}(1+q^{2})^{2}\cdots(1+q^{n})^{2}}.\] It is known that… Expand

## Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function

- S. Ahlgren, Nickolas Andersen
- Mathematics
- 6 December 2013

We construct a natural basis for the space of weak harmonic Maass forms of weight 5/2 on the full modular group. The nonholomorphic part of the first element of this basis encodes the values of the… Expand

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