20132020

Research output per year

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Research Output

  • 22 Article (Academic Journal)
  • 1 Chapter in a book
  • 1 Conference Contribution (Conference Proceeding)
2020

Improved bounds on Brun's constant

Platt, D. & Trudgian, T., 26 Mar 2020, From Analysis to Visualization: A Celebration of the Life and Legacy of Jonathan M. Borwein, Callaghan, Australia, September 2017. Bailey, D. H., Borwein, N. S., Brent, R. P., Burachik, R. S., Osborn, J. H., Sims, B. & Zhu, Q. J. (eds.). Springer-Verlag Berlin, Vol. 313. p. 395-406 (Springer Proceedings in Mathematics and Statistics; vol. 313).

Research output: Chapter in Book/Report/Conference proceedingChapter in a book

Improved bounds on Brun’s constant

Platt, D. & Trudgian, T., 1 Jan 2020, From Analysis to Visualization - A Celebration of the Life and Legacy of Jonathan M. Borwein, 2017. Bailey, D. H., Borwein, N. S., Brent, R. P., Burachik, R. S., Osborn, J. H., Sims, B. & Zhu, Q. J. (eds.). Springer, p. 395-406 12 p. (Springer Proceedings in Mathematics and Statistics; vol. 313).

Research output: Chapter in Book/Report/Conference proceedingConference Contribution (Conference Proceeding)

The Riemann hypothesis is true up to 3 x 10^12

Platt, D. J. & Trudgian, T., 21 Apr 2020, (Submitted) In : arXiv.

Research output: Contribution to journalArticle (Academic Journal)

2019

Fujii's development on Chebyshev's conjecture

Platt, D. J. & Trudgian, T., 1 Apr 2019, In : International Journal of Number Theory. 15, 3, p. 639-644 6 p.

Research output: Contribution to journalArticle (Academic Journal)

Open Access
File
100 Downloads (Pure)

Sign changes in the prime number theorem

Platt, D. J. & Trudgian, T., 2019, (Submitted) In : arXiv.

Research output: Contribution to journalArticle (Academic Journal)

The mean square of the error term in the prime number theorem

Platt, D. J. & Trudgian, T., 2019, (In preparation) In : TBC.

Research output: Contribution to journalArticle (Academic Journal)

Turing’s Method for the Selberg Zeta-Function

Booker, A. & Platt, D. J., 24 Jan 2019, In : Communications in Mathematical Physics. 365, 1, p. 295-328 34 p.

Research output: Contribution to journalArticle (Academic Journal)

Open Access
File
196 Downloads (Pure)
2018

A conjectural extension of Hecke’s converse theorem

Bettin, S., Bober, J., Booker, A., Conrey, B., Lee, M., Molteni, G., Oliver, T., Platt, D. J. & Steiner, R., Dec 2018, In : Ramanujan Journal. 47, 3, p. 659-684 26 p.

Research output: Contribution to journalArticle (Academic Journal)

Open Access
File
2 Citations (Scopus)
216 Downloads (Pure)

Robin's inequality for 20-free integers

Platt, D. J. & Morrill, T., 8 Oct 2018, (Submitted) In : arXiv.

Research output: Contribution to journalArticle (Academic Journal)

The error term in the prime number theorem

Platt, D. J. & Trudgian, T., 10 Sep 2018, (Submitted) In : arXiv.

Research output: Contribution to journalArticle (Academic Journal)

2017

Explicit estimates: from Λ(n) in arithmetic progressions to Λ(n)/n

Platt, D. J. & Ramaré, O., 18 Jan 2017, In : Experimental Mathematics. 26, 1, p. 77-92 15 p.

Research output: Contribution to journalArticle (Academic Journal)

Open Access
File
3 Citations (Scopus)
234 Downloads (Pure)

Isolating some non-trivial zeros of Zeta

Platt, D. J., 6 May 2017, In : Mathematics of Computation. 86, 307, p. 2449-2467 19 p.

Research output: Contribution to journalArticle (Academic Journal)

Open Access
File
5 Citations (Scopus)
368 Downloads (Pure)

On the Sum of Two Squares and At Most Two Powers of 2

Platt, D. & Trudgian, T., Oct 2017, In : American Mathematical Monthly. 124, 8, p. 737-740 4 p.

Research output: Contribution to journalArticle (Academic Journal)

Open Access
File
1 Citation (Scopus)
210 Downloads (Pure)
2016

Diophantine quintuples containing triples of the first kind

Platt, D. J. & Trudgian, T., 1 Jun 2016, In : Periodica Mathematica Hungarica. 72, 2, p. 235-242 8 p.

Research output: Contribution to journalArticle (Academic Journal)

Open Access
File
1 Citation (Scopus)
211 Downloads (Pure)

Numerical Computations Concerning the GRH

Platt, D. J., Nov 2016, In : Mathematics of Computation. 85, 302, p. 3009-3027 19 p.

Research output: Contribution to journalArticle (Academic Journal)

Open Access
File
8 Citations (Scopus)
262 Downloads (Pure)

On the sum of the square of a prime and a square-free number

Dudek, A. & Platt, D. J., 1 Feb 2016, In : LMS Journal of Computation and Mathematics. 19, 1, p. 16-24 9 p.

Research output: Contribution to journalArticle (Academic Journal)

Open Access
File
258 Downloads (Pure)

Zeroes of partial sums of the zeta-function

Platt, D. J. & Trudgian, T., 29 Feb 2016, In : LMS Journal of Computation and Mathematics. 19, 1, p. 37-41 5 p.

Research output: Contribution to journalArticle (Academic Journal)

Open Access
File
1 Citation (Scopus)
296 Downloads (Pure)
2015

An improved explicit bound on $|ζ(1/2 + it)|$

Platt, D. J. & Trudgian, T., Feb 2015, In : Journal of Number Theory. 147, p. 842-851 10 p., MR3276357.

Research output: Contribution to journalArticle (Academic Journal)

8 Citations (Scopus)

Computing π(x) analytically

Platt, D. J., 2015, In : Mathematics of Computation. 84, p. 1521-1535 15 p., MR3315519.

Research output: Contribution to journalArticle (Academic Journal)

11 Citations (Scopus)

Linnik's approximation to Goldbach's conjecture, and other problems

Platt, D. J. & Trudgian, T., 2015, In : Journal of Number Theory. 153, p. 54-62 9 p.

Research output: Contribution to journalArticle (Academic Journal)

7 Citations (Scopus)

On Solving a Curious Inequality of Ramanujan

Dudek, A. & Platt, D. J., 2015, In : Experimental Mathematics. 24, 3, p. 289-294 11 p.

Research output: Contribution to journalArticle (Academic Journal)

1 Citation (Scopus)

On the first sign change of θ(x)-x

Platt, D. J. & Trudgian, T., 21 Aug 2015, In : Mathematics of Computation. 85, p. 1539-1547 9 p.

Research output: Contribution to journalArticle (Academic Journal)

Open Access
File
15 Citations (Scopus)
198 Downloads (Pure)
2013

Explicit Upper Bounds for |L(1, χ)| when χ(3)=0

Platt, D. J. & Saad Eddin, S., 14 Nov 2013, In : Colloquium mathematicum. 133, 1, p. 23-34 12 p., MR3139413.

Research output: Contribution to journalArticle (Academic Journal)

5 Citations (Scopus)

Numerical Verification of the Ternary Goldbach Conjecture up to 8.875 . 10(30)

Helfgott, H. A. & Platt, D. J., 9 Dec 2013, In : Experimental Mathematics. 22, 4, p. 406-409 4 p., MR3171101.

Research output: Contribution to journalArticle (Academic Journal)

4 Citations (Scopus)