An improved upper bound for the error in the zero-counting formulae for Dirichlet $L$-functions and Dedekind zeta-functions
HTML articles powered by AMS MathViewer
- by T. S. Trudgian PDF
- Math. Comp. 84 (2015), 1439-1450 Request permission
Abstract:
This paper contains new explicit upper bounds for the number of zeroes of Dirichlet $L$-functions and Dedekind zeta-functions in rectangles.References
- R. J. Backlund, Über die Nullstellen der Riemannschen Zetafunktion, Acta Math. 41 (1916), no. 1, 345–375 (German). MR 1555156, DOI 10.1007/BF02422950
- Habiba Kadiri and Nathan Ng, Explicit zero density theorems for Dedekind zeta functions, J. Number Theory 132 (2012), no. 4, 748–775. MR 2887617, DOI 10.1016/j.jnt.2011.09.002
- Kevin S. McCurley, Explicit estimates for the error term in the prime number theorem for arithmetic progressions, Math. Comp. 42 (1984), no. 165, 265–285. MR 726004, DOI 10.1090/S0025-5718-1984-0726004-6
- F. W. J. Olver, Asymptotics and special functions, Computer Science and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1974. MR 0435697
- Hans Rademacher, On the Phragmén-Lindelöf theorem and some applications, Math. Z 72 (1959/1960), 192–204. MR 0117200, DOI 10.1007/BF01162949
- Barkley Rosser, Explicit bounds for some functions of prime numbers, Amer. J. Math. 63 (1941), 211–232. MR 3018, DOI 10.2307/2371291
- Timothy Trudgian, An improved upper bound for the argument of the Riemann zeta-function on the critical line, Math. Comp. 81 (2012), no. 278, 1053–1061. MR 2869049, DOI 10.1090/S0025-5718-2011-02537-8
Additional Information
- T. S. Trudgian
- Affiliation: Mathematical Sciences Institute, The Australian National University, Canberra, Australia, 0200
- MR Author ID: 909247
- Email: timothy.trudgian@anu.edu.au
- Received by editor(s): June 8, 2012
- Received by editor(s) in revised form: November 7, 2012, April 16, 2013, and August 12, 2013
- Published electronically: September 15, 2014
- Additional Notes: Supported by Australian Research Council DECRA Grant DE120100173.
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 84 (2015), 1439-1450
- MSC (2010): Primary 11M06; Secondary 11M26, 11R42
- DOI: https://doi.org/10.1090/S0025-5718-2014-02898-6
- MathSciNet review: 3315515