C. Turnage-Butterbaugh

activity

20132026

most citedHilbert transforms and the equidistribution of zeros of polynomials

12 citations · 53 across the 21 of their papers we have counts for

collaborators

24 papers

math.NT2026

A decades-long breakthrough in zero-density estimates and primes in short intervals

Caroline L. Turnage-Butterbaugh

The Riemann Hypothesis (RH) asserts that every nontrivial zero of the Riemann zeta-function has real part equal to $1/2$ . A zero-density theorem provides evidence towards RH by bou…

math.NT2026

Critical Zeros and Unconditional Mean Value Theorems for twisted $PGL (2)$ and $PGL (3)$ $L$ -functions

Brian Conrey, Chung-Hang Kwan, Yongxiao Lin +1

Let $Π_{0}$ be a cuspidal automorphic representation of $PGL_{3} (A_{Q})$ . In this paper, we use Levinson's method to prove that, as $Q \to \infty$ , at lea…

math.NT2025

Short mollifiers of the Riemann zeta-function

J. Brian Conrey, David W. Farmer, Chung-Hang Kwan +2

We apply the calculus of variations to construct a new sequence of linear combinations of derivatives of the Riemann $ζ$ -function adapted to Levinson's method, which yield a positi…

math.NT2025

The Alternative Hypothesis for Zeros of the Riemann Zeta-Function

Siegfred Alan C. Baluyot, Daniel Alan Goldston, Ade Irma Suriajaya +1

In 2016, the first-named author introduced a formulation of the Alternative Hypothesis that assumes that consecutive zeros of the Riemann zeta-function are spaced at multiples of h…

eess.SY2025

Set-based state estimation of nonlinear discrete-time systems using constrained zonotopes and polyhedral relaxations

Brenner S. Rego, Guilherme V. Raffo, Marco H. Terra +1

This paper presents a new algorithm for set-based state estimation of nonlinear discrete-time systems. A key step in such algorithms is to propagate a set (often a zonotope or cons…

math.NT2025

Pair Correlation of Zeros of the Riemann Zeta Function I: Proportions of Simple Zeros and Critical Zeros

Siegfred Alan C. Baluyot, Daniel Alan Goldston, Ade Irma Suriajaya +1

Assuming the Riemann Hypothesis (RH), Montgomery proved a theorem in 1973 concerning the pair correlation of zeros of the Riemann zeta-function and applied this to prove that at le…

math.NT2023★ 9 cited

An unconditional Montgomery Theorem for Pair Correlation of Zeros of the Riemann Zeta Function

Siegfred Alan C. Baluyot, Daniel Alan Goldston, Ade Irma Suriajaya +1

Assuming the Riemann Hypothesis (RH), Montgomery proved a theorem concerning pair correlation of zeros of the Riemann zeta-function. One consequence of this theorem is that, assumi…

math.NT2022★ 1 cited

Twisted $2 k$ th moments of primitive Dirichlet $L$ -functions: beyond the diagonal

Siegfred Baluyot, Caroline L. Turnage-Butterbaugh

We study the family of Dirichlet $L$ -functions of all even primitive characters of conductor at most $Q$ , where $Q$ is a parameter tending to $\infty$ . For an arbitrary positive in…

math.NT2022★ 1 cited

On the Montgomery-Odlyzko method regarding gaps between zeros of the zeta-function

Daniel A. Goldston, Timothy S. Trudgian, Caroline L. Turnage-Butterbaugh

Assuming the Riemann Hypothesis, it is known that there are infinitely many consecutive pairs of zeros of the Riemann zeta-function within 0.515396 times the average spacing. This…

math.CA2021★ 12 cited

Hilbert transforms and the equidistribution of zeros of polynomials

Emanuel Carneiro, Mithun Kumar Das, Alexandra Florea +5

We improve the current bounds for an inequality of Erdős and Turán from 1950 related to the discrepancy of angular equidistribution of the zeros of a given polynomial. Building upo…

math.NT2020

Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function

A. Simonič, T. Trudgian, C. L. Turnage-Butterbaugh

We make explicit an argument of Heath-Brown concerning large and small gaps between nontrivial zeroes of the Riemann zeta-function, $ζ (s)$ . In particular, we provide the first unco…

math.NT2019★ 2 cited

A note on small gaps between zeros of the Riemann zeta-function

D. A. Goldston, C. L. Turnage-Butterbaugh

Assuming the Riemann Hypothesis, we improve on previous results by proving there are infinitely many zeros of the Riemann zeta-function whose differences are smaller than 0.50412 t…

math.NT2019★ 1 cited

On a conjecture for $ℓ$ -torsion in class groups of number fields: from the perspective of moments

Lillian B. Pierce, Caroline L. Turnage-Butterbaugh, Melanie Matchett Wood

It is conjectured that within the class group of any number field, for every integer $ℓ \geq 1$ , the $ℓ$ -torsion subgroup is very small (in an appropriate sense, relative to…

math.NT2018★ 1 cited

Extremal primes of elliptic curves without complex multiplication

C. David, A. Gafni, A. Malik +2

Fix an elliptic curve E over Q. An extremal prime for E is a prime p of good reduction such that the number of rational points on E modulo p is maximal or minimal in relation to th…

math.NT2017

An effective Chebotarev density theorem for families of number fields, with an application to $ℓ$ -torsion in class groups

Lillian B. Pierce, Caroline L. Turnage-Butterbaugh, Melanie Matchett Wood

We prove a new effective Chebotarev density theorem for Galois extensions $L / Q$ that allows one to count small primes (even as small as an arbitrarily small power of the d…

math.NT2016

Some Results in the Theory of Low-lying Zeros: Determining the 1-level density, identifying the group symmetry and the arithmetic of moments of Satake parameters

Blake Mackall, Steven J. Miller, Christina Rapti +5

While Random Matrix Theory has successfully modeled many quantities of families of L-functions, it frequently cannot see the family's arithmetic. In some situations this requires a…

math.NT2015

From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond

Owen Barrett, Frank W. K. Firk, Steven J. Miller +1

The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observati…

math.NT2015★ 1 cited

Gaussian Distribution of the Number of Summands in Generalized Zeckendorf Decompositions in Small Intervals

Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5

Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of non-consecutive Fibonacci numbers $F_{n}$ , with initial terms $F_{1} = 1, F_{2} = 2$ . Previo…

math.NT2014

Benford Behavior of Generalized Zeckendorf Decompositions

Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5

We prove connections between Zeckendorf decompositions and Benford's law. Recall that if we define the Fibonacci numbers by $F_{1} = 1, F_{2} = 2$ and $F_{n + 1} = F_{n} + F_{n - 1}$ , every…

math.NT2014★ 3 cited

Gaps between zeros of GL(2) $L$ -functions

Owen Barrett, Brian McDonald, Steven J. Miller +3

Let $L (s, f)$ be an $L$ -function associated to a primitive (holomorphic or Maass) cusp form $f$ on GL(2) over $Q$ . Combining mean-value estimates of Montgomery and Vaughan…

math.NT2014★ 2 cited

Gaps between zeros of Dedekind zeta-functions of quadratic number fields. II

H. M. Bui, Winston Heap, Caroline L. Turnage-Butterbaugh

Let $K$ be a quadratic number field and $ζ_{K} (s)$ be the associated Dedekind zeta-function. We show that there are infinitely many normalized gaps between consecutive zeros of $ζ_K(…

math.NT2014★ 10 cited

Gaussian Behavior of the Number of Summands in Zeckendorf Decompositions in Small Intervals

Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5

Zeckendorf's theorem states that every positive integer can be written uniquely as a sum of non-consecutive Fibonacci numbers $F_{n}$ , with initial terms $F_{1} = 1, F_{2} = 2$ . We con…

math.NT2014

Benford Behavior of Zeckendorf Decompositions

Andrew Best, Patrick Dynes, Xixi Edelsbrunner +5

A beautiful theorem of Zeckendorf states that every integer can be written uniquely as the sum of non-consecutive Fibonacci numbers ${F_{i}}_{i = 1}^{\infty}$ . A set $S \subset \…

math.NT2013★ 10 cited

Consecutive primes in tuples

William D. Banks, Tristan Freiberg, Caroline L. Turnage-Butterbaugh

In a recent advance towards the Prime $k$ -tuple Conjecture, Maynard and Tao have shown that if $k$ is sufficiently large in terms of $m$ , then for an admissible $k$ -tuple $\mathcal…

A decades-long breakthrough in zero-density estimates and primes in short intervals

Critical Zeros and Unconditional Mean Value Theorems for twisted PGL(2) and PGL(3) L-functions

Short mollifiers of the Riemann zeta-function

The Alternative Hypothesis for Zeros of the Riemann Zeta-Function

Set-based state estimation of nonlinear discrete-time systems using constrained zonotopes and polyhedral relaxations

Pair Correlation of Zeros of the Riemann Zeta Function I: Proportions of Simple Zeros and Critical Zeros

An unconditional Montgomery Theorem for Pair Correlation of Zeros of the Riemann Zeta Function

Twisted 2kth moments of primitive Dirichlet L-functions: beyond the diagonal

On the Montgomery-Odlyzko method regarding gaps between zeros of the zeta-function

Hilbert transforms and the equidistribution of zeros of polynomials

Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function

A note on small gaps between zeros of the Riemann zeta-function

On a conjecture for ℓ-torsion in class groups of number fields: from the perspective of moments

Extremal primes of elliptic curves without complex multiplication

An effective Chebotarev density theorem for families of number fields, with an application to ℓ-torsion in class groups

Some Results in the Theory of Low-lying Zeros: Determining the 1-level density, identifying the group symmetry and the arithmetic of moments of Satake parameters

From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond

Gaussian Distribution of the Number of Summands in Generalized Zeckendorf Decompositions in Small Intervals

Benford Behavior of Generalized Zeckendorf Decompositions

Gaps between zeros of GL(2) L-functions

Gaps between zeros of Dedekind zeta-functions of quadratic number fields. II

Gaussian Behavior of the Number of Summands in Zeckendorf Decompositions in Small Intervals

Benford Behavior of Zeckendorf Decompositions

Consecutive primes in tuples

Critical Zeros and Unconditional Mean Value Theorems for twisted $PGL (2)$ and $PGL (3)$ $L$ -functions

Twisted $2 k$ th moments of primitive Dirichlet $L$ -functions: beyond the diagonal

On a conjecture for $ℓ$ -torsion in class groups of number fields: from the perspective of moments

An effective Chebotarev density theorem for families of number fields, with an application to $ℓ$ -torsion in class groups

Gaps between zeros of GL(2) $L$ -functions