Date: 16 Nov 2010
A short proof of Levinson’s theorem
- Matthew P. Young
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
We give a short proof of Levinson’s result that over 1/3 of the zeros of the Riemann zeta function are on the critical line.
This material is based upon work supported by the National Science Foundation under agreement Nos. DMS-0758235 and DMS-0635607. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
- Conrey, J.B. (1989) More than two fifths of the zeros of the Riemann zeta function are on the critical line. J. Reine Angew. Math. 399: pp. 1-26
- Conrey, J.B. (1983) Zeros of derivatives of Riemann’s ξ-function on the critical line. J. Number Theory 16: pp. 49-74 CrossRef
- J. B. Conrey and A. Ghosh, A simpler proof of Levinson’s theorem, Math. Proc. Cambridge Philos. Soc. 97 (1985), 385–395. Proc. Lond. Math. Soc. (3) 94 (2007), 594–646.
- Ivić, A. (1985) The Riemann zeta-function, The theory of the Riemann zeta-function with applications. John Wiley & Sons. Inc., New York
- H. Iwaniec and E. Kowalski, Analytic Number Theory, American Mathematical Society Colloquium Publications, 53. American Mathematical Society, Providence, RI, 2004.
- A. Karatsuba and S. Voronin, The Riemann zeta-function, Translated from the Russian by Neal Koblitz, de Gruyter Expositions in Mathematics, 5, Walter de Gruyter & Co., Berlin, 1992.
- Levinson, N. (1974) More than one third of the zeros of Riemann’s zeta function are on σ = 1/2. Adv. Math. 13: pp. 383-436 CrossRef
- A. Selberg, On the zeros of Riemann’s zeta-function, Skr. Norske Vid. Akad. Oslo I. (1942), 1–59.
- E. C. Titchmarsh, The Theory of the Riemann Zeta-function, 2nd ed., Edited and with a preface by D. R. Heath-Brown, The Clarendon Press, Oxford University Press, New York, 1986.
- A short proof of Levinson’s theorem
Archiv der Mathematik
Volume 95, Issue 6 , pp 539-548
- Cover Date
- Print ISSN
- Online ISSN
- SP Birkhäuser Verlag Basel
- Additional Links
- Primary 11M26
- Riemann zeta function
- Critical line
- Mean value
- Matthew P. Young (1) (2)
- Author Affiliations
- 1. Department of Mathematics, Texas A&M University, College Station, TX, 77843-3368, USA
- 2. School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, NJ, 08540, USA