I. Mercer

activity

20122017

most citedDirichlet's theorem and Jacobsthal's function

1 citations · 1 across the 5 of their papers we have counts for

collaborators

5 papers

math.NT2017

Finite searches, Chowla's cosine problem, and large Newman polynomials

Idris Mercer

A length $n$ cosine sum is an expression of the form $cos a_{1} θ + \dots + cos a_{n} θ$ where $a_{1} < \dots < a_{n}$ are positive integers, and a length $n$ Newman polynomial is an expr…

math.NT2017★ 1 cited

Dirichlet's theorem and Jacobsthal's function

Idris Mercer

If $a$ and $d$ are relatively prime, we refer to the set of integers congruent to $a$ mod $d$ as an `eligible' arithmetic progression. A theorem of Dirichlet says that every eligib…

cs.IT2016

A unified approach to autocorrelation of Frank, Chu, and Milewski sequences

Idris Mercer

We construct a family of perfect polyphase sequences that has the Frank sequences, Chu sequences, and Milewski sequences as special cases. This is not the most general construction…

math.CO2015

Improved bounds on the peak sidelobe level of binary sequences

Idris Mercer

Schmidt proved in 2014 that if $ε > 0$ , almost all binary sequences of length $n$ have peak sidelobe level between $(2 - ε) n lo g n$ and $(\sqrt{2}+\va…

math.CA2012

On a function related to Chowla's cosine problem

Idris Mercer

Chowla's cosine problem concerns the largest minimum of an expression of the form $cos a_{1} θ + ... + cos a_{n} θ$ where the $a_{i}$ are distinct positive integers. We compute this large…