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THE $\unicode[STIX]{x1D703}=\infty$ CONJECTURE IMPLIES THE RIEMANN HYPOTHESIS

  • Sandro Bettin (a1) and Steven M. Gonek (a2)

Abstract

We show that the $\unicode[STIX]{x1D703}=\infty$ conjecture implies the Riemann hypothesis.

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References

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1. Conrey, J. B., More than two fifths of the zeros of the Riemann zeta function are on the critical line. J. Reine Angew. Math. 399 1989, 126.
2. Farmer, D. W., Long mollifiers of the Riemann zeta-function. Mathematika 40(1) 1993, 7187.
3. Gonek, S. M., Graham, S. W. and Lee, Y., A Generalized Lindelöf Hypothesis, unpublished manuscript.
4. Levinson, N., More than one third of zeros of Riemann’s zeta-function are on 𝜎 = 1/2. Adv. Math. 13 1974, 383436.
5. Pintz, J., Oscillatory properties of M (x) =∑ nx 𝜇(n). I. Acta Arith. 42(1) 1982/1983, 4955.
6. Radziwiłł, M., Limitations to mollifying $\unicode[STIX]{x1D701}(s)$ , Preprint 2012, arXiv:math.NT/1207.6583.
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Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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