Olivia Beckwith

activity

20112026

most citedThe Average Gap Distribution for Generalized Zeckendorf Decompositions

26 citations · 52 across the 18 of their papers we have counts for

collaborators

19 papers

math.NT2026

Selmer groups of CM-twists of elliptic curves

Olivia Beckwith, Tùng Hoàng

Let $F$ be a totally real Galois number field of degree $g \leq 5$ and let $ℓ$ be an odd prime. Let $E / F$ be an elliptic curve with an $F$ -rational point of order $ℓ$ . Under ex…

math.NT2026

Riesz Means of Quadratic Class Numbers

Olivia Beckwith, Tushar Karmakar

We prove an asymptotic formula for a weighted Riesz mean of Hurwitz class numbers and real quadratic class numbers. To do this, we introduce L-functions for weight $\frac{1}{2}$ …

math.NT2023

Imaginary quadratic fields with $ℓ$ -torsion-free class groups and specified split primes

Olivia Beckwith, Martin Raum, Olav Richter

Given an odd prime $ℓ$ and finite set of odd primes $S_{+}$ , we prove the existence of an imaginary quadratic field whose class number is indivisible by $ℓ$ and which splits at…

math.NT2022

Theta-type congruences for colored partitions

Olivia Beckwith, Alexander Caione, Jack Chen +3

We investigate congruence relations of the form $p_{r} (ℓ mn + t) \equiv 0 (mod ℓ)$ for all $n$ , where $p_{r} (n)$ is the number of $r$ -colored partitions of $n$ and $m, ℓ$ are…

math.NT2022

Congruences of Hurwitz class numbers on square classes

Olivia Beckwith, Martin Raum, Olav Richter

We extend a holomorphic projection argument of our earlier work to prove a novel divisibility result for non-holomorphic congruences of Hurwitz class numbers. This result allows us…

math.NT2022

Integer partitions with large Dyson rank

Colin Alberts, Olivia Beckwith, Irfan Demetoglu +3

The Dyson rank of an integer partition is the difference between its largest part and the number of parts it contains. Using Fine-Dyson symmetry, we give formulas for the number of…

math.NT2021★ 2 cited

A zero density estimate and fractional imaginary parts of zeros for $GL_{2}$ $L$ -functions

Olivia Beckwith, Di Liu, Jesse Thorner +1

We prove an analogue of Selberg's zero density estimate for $ζ (s)$ that holds for any $GL_{2}$ $L$ -function. We use this estimate to study the distribution of the vector of…

math.NT2020★ 1 cited

Scarcity of congruences for the partition function

Scott Ahlgren, Olivia Beckwith, Martin Raum

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…

math.NT2020★ 4 cited

Non-Holomorphic Ramanujan-type Congruences for Hurwitz Class Numbers

Olivia Beckwith, Martin Raum, Olav K. Richter

In contrast to all other known Ramanujan-type congruences, we discover that Ramanujan-type congruences for Hurwitz class numbers can be supported on non-holomorphic generating seri…

math.NT2018

Class number divisibility for imaginary quadratic fields

Olivia Beckwith

In this note we revisit classic work of Soundararajan on class groups of imaginary quadratic fields. Let $A, B, g \geq 3$ be positive integers such that $g cd (A, B)$ is square-free. We…

math.NT2016★ 1 cited

Indivisibility of class numbers of imaginary quadratic fields

Olivia Beckwith

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 whose cl…

math.NT2016

Asymptotic bounds for special values of shifted convolution Dirichlet series

Olivia Beckwith

Hoffstein and Hulse defined the shifted convolution series of two cusp forms by "shifting" the usual Rankin-Selberg convolution L-series by a parameter h. We use the theory of harm…

math.NT2016★ 3 cited

On the number of parts of integer partitions lying in given residue classes

Olivia Beckwith, Michael Mertens

Improving upon previous work 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 that are in any g…

math.NT2015★ 5 cited

The Number of Parts in Certain Residue Classes of Integer Partitions

Olivia Beckwith, Michael Mertens

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

math.NT2014

Multiplicative properties of the number of $k$ -regular partitions

Olivia Beckwith, Christine Bessenrodt

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. Exte…

math.NT2012★ 26 cited

The Average Gap Distribution for Generalized Zeckendorf Decompositions

Olivia Beckwith, Amanda Bower, Louis Gaudet +4

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 un…

math.CO2012★ 8 cited

Minkowski length of 3D lattice polytopes

Olivia Beckwith, Matthew Grimm, Jenya Soprunova +1

We study the Minkowski length L(P) of a lattice polytope P, which is defined to be the largest number of non-trivial primitive segments whose Minkowski sum lies in P. The Minkowski…

math.PR2011★ 2 cited

Distribution of Eigenvalues of Weighted, Structured Matrix Ensembles

Olivia Beckwith, Victor Luo, Steven J. Miller +2

The limiting distribution of eigenvalues of N x N random matrices has many applications. One of the most studied ensembles are real symmetric matrices with independent entries iidr…

math.NT2011

Generalized Ramanujan Primes

Nadine Amersi, Olivia Beckwith, Steven J. Miller +2

In 1845, Bertrand conjectured that for all integers $x \geq 2$ , there exists at least one prime in $(x /2, x]$ . This was proved by Chebyshev in 1860, and then generalized by Ramanujan…

Selmer groups of CM-twists of elliptic curves

Riesz Means of Quadratic Class Numbers

Imaginary quadratic fields with ℓ-torsion-free class groups and specified split primes

Theta-type congruences for colored partitions

Congruences of Hurwitz class numbers on square classes

Integer partitions with large Dyson rank

A zero density estimate and fractional imaginary parts of zeros for GL2​ L-functions

Scarcity of congruences for the partition function

Non-Holomorphic Ramanujan-type Congruences for Hurwitz Class Numbers

Class number divisibility for imaginary quadratic fields

Indivisibility of class numbers of imaginary quadratic fields

Asymptotic bounds for special values of shifted convolution Dirichlet series

On the number of parts of integer partitions lying in given residue classes

The Number of Parts in Certain Residue Classes of Integer Partitions

Multiplicative properties of the number of k-regular partitions

The Average Gap Distribution for Generalized Zeckendorf Decompositions

Minkowski length of 3D lattice polytopes

Distribution of Eigenvalues of Weighted, Structured Matrix Ensembles

Generalized Ramanujan Primes

Imaginary quadratic fields with $ℓ$ -torsion-free class groups and specified split primes

A zero density estimate and fractional imaginary parts of zeros for $GL_{2}$ $L$ -functions

Multiplicative properties of the number of $k$ -regular partitions