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Experimental Mathematics Volume 24, 2015 - Issue 3
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Original Articles

On Solving a Curious Inequality of Ramanujan

Adrian W. DudekMathematical Sciences Institute, Australian National University, Canberra, AustraliaCorrespondence[email protected]
&
David J. PlattHeilbronn Institute for Mathematical Research, University of Bristol, Bristol, UK
Pages 289-294 | Published online: 23 Jun 2015

References

  • [Berndt 93] B. C. Berndt. Ramanujan’s Notebooks: Part IV. Springer, 1993.
  • [Hassani 12] Mehdi Hassani. “On an Inequality of Ramanujan Concerning the Prime Counting Function.” Ramanujan Journal 28 (2012), 435–442.
  • [Montgomery and Vaughan 73] H. L. Montgomery and R. C. Vaughan. “The Large Sieve.” Mathematika 20 (1973), 119–134.
  • [Mossinghoff and Trudgian 14] M. J. Mossinghoff and T. S. Trudgian. “Nonnegative Trigonometric Polynomials and a Zero-Free Region for the Riemann Zeta-Function.” arXiv: 1410.3926, 2014.
  • [Oliveira e Silva 12] T. Oliveira e Silva. “Tables of Values of π(x) and π2(x)”. Available online (http://www.ieeta.pt/ tos/primes.html), 2012.
  • [Platt and Trudgian 15] D. J. Platt and T. S. Trudgian. “On the First Sign Change of θ(x) − x.” To appear in Math. Comp.
  • [Schoenfeld 76] L Schoenfeld. “Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II.” Math. Comp. 30 (1976), 337–360.
  • [Trudgian 14] T. S. Trudgian. “Updating the Error Term in the Prime Number Theorem.” To appear in Ramanujan J., 2014.

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