Zeros of dirichlet L-functions near the real axis and chebyshev’s bias

Journal of Number Theory

Volumn 87, Issue 1, 2001, Pages 54-76

  Bays, Carter ^a,b   Ford, Kevin ^a,b   Hudson, Richard H ^a,b   Rubinstein, Michael ^a,b  

^a UNIVERSITY OF SOUTH CAROLINA   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038979252     PISSN: 0022314X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jnth.2000.2601     Document Type: Article

References (41)

1. Arno S., Robinson M. L., Wheeler F. S. Imaginary quadratic fields with small odd class number. Acta Arith. 83:1998;295-330
2. Arno S. The imaginary quadratic fields of class number 4. Acta Arith. 60:1992;321-334
3. 3, 1(x). Math. Comp. 32:1978;571-576
4. 12Internat. J. Math. Math. Sci. 2:1979;111-119
5. Bays C., Hudson R. H. Zeros of Dirichlet L-functions and irregularities in the distribution of primes. Math. Comp. 69:2000;861-866
6. Bays C., Hudson R. H. A new bound for the smallest x with π(x)>li(x). Math. Comp. 69:2000;1285-1296
7. Borevich Z. I., Shavarevich I. R. Number Theory. 1966;Academic Press, New York
8. Chowla S., Selberg A. On Epstein’s zeta-function. J. Reine Angew. Math. 227:1967;86-110
9. Chébyshev P. L. Lettre de M. le Professor Tchébychev à M. Fuss sur un nouveaux théorème relatif aux nombres premiers contenus dans les formes 4n+1 ets 4n+3. Bull. Classe Phys. Acad. Imp. Sci. St. Petersburg. 11:1853;208
10. Davenport H. Multiplicative Number Theory. Graduate Texts in Mathematics. 74:1980;Springer-Verlag, Berlin
11. q, b(x), submitted for publication
12. Gross B., Zagier D. Heegner Points and Derivatives of L-series. Invent. Math. 84:1986;225-320
13. Hudson R. H. The mean behavior of primes in arithmetic progressions. J. Reine Angew. Math. 296:1977;80-99
14. Hudson R. H. A formula for the exact number of primes below a given limit any arithmetic progression. Bull. Austral. Math. Soc. 16:1977;67-73
15. Hudson R. H. A common combinatorial principle underlies Riemann’s formula, the Chebyshev phenomenon, and other subtle effects in comparative prime number theory, I. J. Reine Angew. Math. 313:1980;133-150
16. Hudson R. H. Averaging effects on irregularities in the distribution of primes in arithmetic progressions. Math. Comp. 44:1985;561-571
17. Kaczorowski J. The boundary values of generalized Dirichlet series and a problem of Chebyshev. Asterisque. 14:1992;227-235
18. Kaczorowski J. A contribution to the Shanks-Renyi race problem. Quart. J. Math., Oxford Ser. (2). 44:1993;451-458
19. Kaczorowski J. On the distribution of primes (mod 4). Analysis. 15:1995;159-171
20. Katz N., Sarnak P. Zeros of zeta functions and symmetry. Bull. Amer. Math. Soc. 39:1999;1-26
21. Knapowski S., Turan P. Comparative prime number theory, I. Acta Math. Hungar. 13:1962;299-314
22. Lagarias J., Miller V., Odlyzko A. Computing π(x): The Meissel-Lehmer method. Math. Comp. 44:1985;537-560
23. Landau E. Handbuch der Lehre von der Verteilung der Primzahlen. 1974;Chelsea, New York
24. Leech J. Note on the distribution of prime numbers. J. London Math. Soc. 32:1957;56-58
25. Lehman R. S. On the difference π(x)-li(x). Acta Arith. 11:1966;397-410
26. Littlewood J. E. Sur la distribution des nombres premiers. Comptes Rendus. 158:1914;1869-1872
27. Meissel E. Über die Bestimmung der Primzahlmenge innerhalf gegebener Grenzen. Math. Ann. 2:1870;636-642
28. Montgomery H. L., Weinberger P. J. Notes on small class numbers. Acta Arith. 24:1974;529-542
29. H. L. Montgomery, The Zeta function and prime numbers, in Proceedings of the Queen’s Number Theory Conference, 1979, pp. 14-24
30. Osluk A. E., Snyder C. Small zeros of quadratic L-functions. Bull. Austral. Math. Soc. 47:1993;307-318
31. B. Riemann, Über die Anzahl der Primzahlen unter einer gegeben Grosse, in Monatsbericht d. preuss. Akad. d. Wissens, Berlin, 1859, 1860, pp. 671-680, Gessamelte Math. Werke (1892), pp. 145-155
32. B. Riemann, Über die Anzahl der Primzahlen unter einer gegeben Grosse, in Monatsbericht d. preuss. Akad. d. Wissens, Berlin, 1859, 1860, pp. 671-680, Gessamelte Math. Werke (1892), pp. 145-155
33. Rubinstein M. Evidence for a Spectral Interpretation of Zeros of L-Functions. 1998;Princeton University
34. Rubinstein M., Sarnak P. Chebyshev’s bias. J. Experiment. Math. 3:1994;173-197
35. Rumely R. Numerical computations concerning the ERH. Math. Comp. 61:1993;415-440
36. Shanks D. Quadratic residues and the distribution of primes. Math. Comp. 13:1959;272-284
37. Stark H. M. On complex quadratic number fields with class number equal to one. Trans. Amer. Math. Soc. 122:1966;112-119
38. Stark H. M. On complex quadratic fields with class number two. Math. Comp. 29:1975;289-302
39. Stark H. M. A complete determination of the complex quadratic fields of class-number one. Michigan Math. J. 14:1967;1-27
40. Watson G. N. A Treatise on the Theory of Bessel Functions. 1966;Cambridge Univ. Press, London
41. Weinberger P. J. On small zeros of Dirichlet L-functions. Math. Comp. 29:1975;319-328