References

CHEBYSHEV'S BIAS AND GENERALIZED RIEMANN HYPOTHESIS


[1] C. Bays and R. H. Hudson, Numerical and graphical description of all axis crossing regions for the moduli 4 and 8 which occurs before Intern. J. Math. & Math. Sci. 2 (1979), 111-119.

[2] C. Bays and R. H. Hudson, A new bound for the smallest x with Math. Comp. 69(231) (2000), 1285-1296.

[3] C. Bays, K. Ford, R. H. Hudson and M. Rubinstein, Zeros of Dirichlet L-functions near the real axis and Chebyshev’s bias, J. Numb. Th. 87 (2001), 54-76.

[4] W. Bosma, J. Cannon and C. Playoust, The Magma algebra system I. The user language, J. Symb. Comput. 24 (1997), 235-265.

[5] H. Davenport, Multiplicative Number Theory, Second Edition, Springer Verlag, New York, 1980.

[6] M. Deléglise, P. Dusart and X.-F. Boblot, Counting primes in residue classes, Math. Comp. 73(247) (2004), 1565-1575.

[7] D. Fiorilli and G. Martin, Inequalities in the Shanks-Rényi prime number-race: An asymptotic formula for the densities, Crelle’s J. (to appear); Preprint 0912.4908 [Math. NT].

[8] A. E. Ingham, The Distribution of Prime Numbers, Mathematical Library, Cambridge University Press, Cambridge, 1990, (Reprint of the 1932 original).

[9] G. Martin, Asymmetries in the Shanks-Rényi prime number race, Number theory for the millenium, II (Urbana, IL, 2000), 403415, A. K. Pters, Natick, MA, 2002.

[10] P. Moree, Chebyshev’s bias for composite numbers with restricted prime divisors, Math. Comp. 73 (2003), 425-449.

[11] M. Planat and P. Solé, Efficient prime counting and the Chebyshev primes, Preprint 1109.6489 (Math. NT).

[12] G. Robin, Sur la difference Ann. Fac. Sc. Toulouse 6 (1984), 257-268.

[13] M. Rubinstein and P. Sarnak, Chebyshev’s bias, Exp. Math. 3(3) (1994), 173-197.