Brad Rodgers

activity

20122026

most citedArithmetic functions in short intervals and the symmetric group

23 citations · 141 across the 21 of their papers we have counts for

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14 papers · 1 filter

math.NT2022★ 1 cited

Averages of quadratic twists of long Dirichlet polynomials

Brian Conrey, Brad Rodgers

We investigate averages of long Dirichlet polynomials twisted by Kronecker symbols and we compare our result with the recipe of [CFKRS]. We are able to compute these averages in th…

math.NT2021

Squarefrees are Gaussian in short intervals

Ofir Gorodetsky, Alexander P. Mangerel, Brad Rodgers

We show that counts of squarefree integers up to $X$ in short intervals of size $H$ tend to a Gaussian distribution as long as $H \to \infty$ and $H = X^{o (1)}$ . This answers…

math.NT2020★ 14 cited

Moments of polynomials with random multiplicative coefficients

Jacques Benatar, Alon Nishry, Brad Rodgers

For $X (n)$ a Rademacher or Steinhaus random multiplicative function, we consider the random polynomials $P_{N} (θ) = \frac{1}{N} n \leq N \sum X (n) e (n θ),$ and show that the…

math.NT2020★ 11 cited

On the variance of squarefree integers in short intervals and arithmetic progressions

Ofir Gorodetsky, Kaisa Matomäki, Maksym Radziwiłł +1

We evaluate asymptotically the variance of the number of squarefree integers up to $x$ in short intervals of length $H < x^{6/11 - ε}$ and the variance of the number of s…

math.NT2020

Sums of singular series and primes in short intervals in algebraic number fields

Vivian Kuperberg, Brad Rodgers, Edva Roditty-Gershon

Gross and Smith have put forward generalizations of Hardy - Littlewood twin prime conjectures for algebraic number fields. We estimate the behavior of sums of a singular series tha…

math.NT2019★ 4 cited

Higher Correlations and the Alternative Hypothesis

Jeffrey C. Lagarias, Brad Rodgers

The Alternative Hypothesis concerns a hypothetical and unlikely picture of how zeros of the Riemann zeta function are spaced which one would like to rule out. In the Alternative Hy…

math.NT2018★ 4 cited

The variance of the number of sums of two squares in $F_{q} [T]$ in short intervals

Ofir Gorodetsky, Brad Rodgers

Consider the number of integers in a short interval that can be represented as a sum of two squares. What is an estimate for the variance of these counts over random short interval…

math.NT2018★ 7 cited

The De Bruijn-Newman constant is non-negative

Brad Rodgers, Terence Tao

For each $t \in R$ , define the entire function $H_{t} (x) := \int_{0}^{\infty} e^{t u^{2}} Φ (u) cos (xu) d u$ where $Φ$ is the super-exponentially decaying function $$ Φ(u) := \sum_…

math.NT2016★ 14 cited

The variance of divisor sums in arithmetic progressions

Brad Rodgers, Kannan Soundararajan

We study the variance of sums of the $k$ -fold divisor function $d_{k} (n)$ over sparse arithmetic progressions, with averaging over both residue classes and moduli. In a restricted ra…

math.NT2016★ 23 cited

Arithmetic functions in short intervals and the symmetric group

Brad Rodgers

We consider the variance of sums of arithmetic functions over random short intervals in the function field setting. Based on the analogy between factorizations of random elements o…

math.NT2015★ 2 cited

Tail bounds for counts of zeros and eigenvalues, and an application to ratios

Brad Rodgers

Let $t$ be random and uniformly distributed in the interval $[T, 2 T]$ , and consider the quantity $N (t + 1/ lo g T) - N (t)$ , a count of zeros of the Riemann zeta function in a box of he…

math.NT2014★ 6 cited

Bootstrapped zero density estimates and a central limit theorem for the zeros of the zeta function

Kenneth Maples, Brad Rodgers

We unconditionally prove a central limit theorem for linear statistics of the zeros of the Riemann zeta function with diverging variance. Previously, theorems of this sort have bee…

math.NT2013★ 5 cited

The covariance of almost-primes in $F_{q} [T]$

Brad Rodgers

We estimate the covariance in counts of almost-primes in $F_{q} [T]$ , weighted by higher-order von Mangoldt functions. The answer takes a pleasant algebraic form. This genera…

math.NT2012★ 12 cited

Macroscopic pair correlation of the Riemann zeroes for smooth test functions

Brad Rodgers

On the assumption of the Riemann hypothesis, we show that over a class of sufficiently smooth test functions, a measure conjectured by Bogomolny and Keating coincides to a very sma…

Averages of quadratic twists of long Dirichlet polynomials

Squarefrees are Gaussian in short intervals

Moments of polynomials with random multiplicative coefficients

On the variance of squarefree integers in short intervals and arithmetic progressions

Sums of singular series and primes in short intervals in algebraic number fields

Higher Correlations and the Alternative Hypothesis

The variance of the number of sums of two squares in Fq​[T] in short intervals

The De Bruijn-Newman constant is non-negative

The variance of divisor sums in arithmetic progressions

Arithmetic functions in short intervals and the symmetric group

Tail bounds for counts of zeros and eigenvalues, and an application to ratios

Bootstrapped zero density estimates and a central limit theorem for the zeros of the zeta function

The covariance of almost-primes in Fq​[T]

Macroscopic pair correlation of the Riemann zeroes for smooth test functions

The variance of the number of sums of two squares in $F_{q} [T]$ in short intervals

The covariance of almost-primes in $F_{q} [T]$