Binary Constant-Length Substitutions and Mahler Measures of Borwein Polynomials

Autor: Baake, Michael, Coons, Michael, Mañibo, Chrizaldy Neil, Bailey, David H., Borwein, Naomi Simone, Brent, Richard P., Burachik, Regina S., Osborn, Judy-anne Heather, Sims, Brailey, Zhu, Qiji J.

Publikováno v: Springer Proceedings in Mathematics & Statistics ISBN: 9783030365677

We show that the Mahler measure of every Borwein polynomial—a polynomial with coefficients in \( \{-1,0,1 \}\) having non-zero constant term—can be expressed as a maximal Lyapunov exponent of a matrix cocycle that arises in the spectral theory of

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::88e736397f707effcf0df902aafd8828
https://doi.org/10.1007/978-3-030-36568-4_20

Improved bounds on Brun's constant

Autor: Platt, Dave, Trudgian, Tim

Publikováno v: Platt, D & Trudgian, T 2020, Improved bounds on Brun's constant . in D H Bailey, N S Borwein, R P Brent, R S Burachik, J H Osborn, B Sims & Q J Zhu (eds), From Analysis to Visualization : A Celebration of the Life and Legacy of Jonathan M. Borwein, Callaghan, Australia, September 2017 . vol. 313, Springer Proceedings in Mathematics and Statistics, vol. 313, Springer-Verlag Berlin, pp. 395-406 . https://doi.org/10.1007/978-3-030-36568-4

Brun’s constant is B = Pp∈P2p−1 + (p + 2)−1, where the summation is over all twin primes. We improve the unconditional bounds on Brun’s constant to 1.840503 < B < 2.288490, which are about 13% tighter.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=od______2642::040eb43c835d371fd52d24a0ebfe67c2
https://research-information.bris.ac.uk/en/publications/e6c3acbe-8271-493a-91d6-4bf49722a3c4