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)
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Article (Academic Journal)
2020

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
113 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
201 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
3 Citations (Scopus)
224 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)
242 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
6 Citations (Scopus)
388 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)
219 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)
223 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)
272 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
267 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)
304 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)

9 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)

8 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)
204 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)