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Multiplicative Properties of the Number of k-Regular Partitions

- Olivia Beckwith, C. Bessenrodt
- Mathematics
- 10 September 2014

In a previous paper of the second author with K. Ono, surprising multiplicative properties of the partition function were presented. Here, we deal with k-regular partitions. Extending the generating… Expand

On the Number of Parts of Integer Partitions Lying in Given Residue Classes

- Olivia Beckwith, Michael H. Mertens
- Mathematics
- 11 February 2016

Improving upon previous work [3] on the subject, we use Wright’s Circle Method to derive an asymptotic formula for the number of parts in all partitions of an integer n that are in any given… Expand

Minkowski Length of 3D Lattice Polytopes

- Olivia Beckwith, M. Grimm, Jenya Soprunova, Bradley Weaver
- MathematicsDiscret. Comput. Geom.
- 2 February 2012

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Distribution of Eigenvalues of Weighted, Structured Matrix Ensembles

- Olivia Beckwith, Victor Luo, S. Miller, Karen Shen, N. Triantafillou
- MathematicsIntegers
- 1 December 2011

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The number of parts in certain residue classes of integer partitions

- Olivia Beckwith, Michael H. Mertens
- Mathematics
- 26 May 2015

We use the Circle Method to derive asymptotics for functions related to the number of parts of partitions in particular residue classes.

The Average Gap Distribution for Generalized Zeckendorf Decompositions

- Olivia Beckwith, Amanda Bower,
+4 authors Philip Tosteson - Mathematics
- 29 August 2012

An interesting characterization of the Fibonacci numbers is that, if we write them as $F_1 = 1$, $F_2 = 2$, $F_3 = 3$, $F_4 = 5, ...$, then every positive integer can be written uniquely as a sum of… Expand

Generalized Ramanujan Primes

- Nadine Amersi, Olivia Beckwith, S. Miller, Ryan Ronan, J. Sondow
- Mathematics
- 2 August 2011

In 1845, Bertrand conjectured that for all integers x ≥ 2, there exists at least one prime in (x∕2, x]. This was proved by Chebyshev in 1860 and then generalized by Ramanujan in 1919. He showed that… Expand

Indivisibility of class numbers of imaginary quadratic fields

- Olivia Beckwith
- Mathematics
- 14 December 2016

We quantify a recent theorem of Wiles on class numbers of imaginary quadratic fields by proving an estimate for the number of negative fundamental discriminants down to $$-X$$-X whose class numbers… Expand

Scarcity of congruences for the partition function

- S. Ahlgren, Olivia Beckwith, Martin Raum
- Mathematics
- 13 June 2020

The arithmetic properties of the ordinary partition function $p(n)$ have been the topic of intensive study for the past century. Ramanujan proved that there are linear congruences of the form $p(\ell… Expand

Nonholomorphic Ramanujan-type congruences for Hurwitz class numbers

- Olivia Beckwith, Martin Raum, Olav K. Richter
- MathematicsProceedings of the National Academy of Sciences
- 15 April 2020

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