Differentiation evens out zero spacings

Transactions of the American Mathematical Society

Volumn 357, Issue 9, 2005, Pages 3789-3811

  Farmer, David W ^a   Rhoades, Robert C ^b  

^a AMERICAN INSTITUTE OF MATHEMATICS   (United States)

^b BUCKNELL UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22244432387     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-05-03721-9     Document Type: Article

References (21)

1. R.P. Boas, Entire Functions, Academic Press, 1954. MR0068627 (16:914f)
2. J.B. Conrey, Zeros of derivatives of Riemann's ξ-function on the critical line, J. Number Theory 16 (1983), no. 1, 49-74. MR0693393 (84g:10070)
3. J.B. Conrey, D.W. Farmer, J. Keating, M. Rubinstein, and N.C. Snaith, Integral moments of families of L-functions, http://arxiv.org/abs/math.NT/0206018.
4. J.B. Conrey and H. Iwaniec, Spacing of zeros of Hecke L-functions and the class number problem, Acta Arith. 103 (2002) no. 3, 259-312. MR1905090 (2003h:11103)
5. T. Craven, G. Csordas, and W. Smith, Zeros of derivatives of entire functions, PAMS 101 (1987), 323-326. MR0902550 (88k:30024)
6. T. Craven, G. Csordas, and W. Smith, Zeros of derivatives of entire functions and the Pólya-Wiman conjecture, Ann. of Math (2) 125 (1987), 405-431. MR0881274 (88a:30007)
7. P. Davis, Circulant Matrices, John Wiley and Sons, 1979. MR0543191 (81a:15003)
8. D.W. Farmer and S.M. Gonek, Pair correlation of the zeros of ξ′, in preparation.
9. H. Ki, personal communication.
10. H. Ki and Y.-O. Kim, On the number of nonreal zeros of real entire functions and the Fourier-Pólya conjecture, Duke Math. J, Vol. 104, No. 1, (2000), 45-73. MR1769725 (2001h:30022)
11. Y.-O. Kim, A proof of the Pólya-Wiman conjecture, PAMS 109 (1990), 1045-1052. MR1013971 (90k:30049)
12. Y.-O. Kim, Critical points of real entire functions and a conjecture of Pólya, PAMS, Vol. 124, No. 3, (1996), 819-829. MR1301508 (96f:30027)
13. R. Kreminski, Newton-Cotes integration for approximating Stieltjes (generalized Euler) constants. Math. Comp. 72 (2003), no. 243, 1379-1397. MR1972742 (2004a:11140)
14. R. Kreminski, http://www.tamu-commerce.edu/coas/math/FACULTY/KREMIN/stieltjesrelated/
15. N. Levinson and H. Montgomery, Zeros of the derivatives of the Riemann zeta-function, Acta Math. 133 (1974), 49-65. MR0417074 (54:5135)
16. G. Pólya, Some problems connected with Fourier's work on transcendental equations, Quart. J. Math. Oxford Ser. (2) 1 (1903), 21-34.
17. T. Sheil-Small, On the zeros of the derivatives of real entire functions and Wiman's conjecture. Ann. of Math. (2) 129 (1989), no. 1, 179-193. MR0979605 (90a:30084)
18. A. Stoyanoff, Sur un Thórem de M. Marcel Riesz, Nouvelles Annales de Mathématique, 1 (1926), 97-99.
19. J.v. Sz.-Nagy, Über Polynome mit lauter reelen Nullstellen, Acta Math. Acad. Scient. Hung. 1 (1950), 225-8. MR0046479 (13:740f)
20. P. Walker, Separation of the zeros of polynomials, Amer. Math. Monthly 100 (1993), no. 3, 272-273. MR1212834
21. P. Walker, Bounds for the separation of real zeros of polynomials, J. Austral. Math. Soc. (Series A) 59 (1995), 330-342. MR1355224 (96i:26017)