152
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

A Refined Conjecture for the Variance of Gaussian Primes across Sectors

, , , , , , , & show all

References

  • Andrade, J. C, Keating, J. P. (2014). Conjectures for the integral moments and ratios of L-functions over function fields. J. Number Theory 142: 102–148. doi:10.1016/j.jnt.2014.02.019
  • Bui, H. M., Keating, J. P, Smith, D. J. (2016). On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class. J. London Math. Soc. 94(1): 161–185. (2) doi:10.1112/jlms/jdw030
  • Conrey, J. B., Farmer, D. W, Zirnbauer, M. R. (2008). Autocorrelation of ratios of L-functions. Commun. Number Theory Phys 2(3): 593–636. doi:10.4310/CNTP.2008.v2.n3.a4
  • Conrey, J. B., Farmer, D. W., Keating, J. P., Rubinstein, M. O, Snaith, N. C. (2005). Integral moments of L-functions. Proc. London Math. Soc. 91(01): 33–104. (3) doi:10.1112/S0024611504015175
  • Conrey, B, Farmer, D. (2000). Mean values of L-functions and symmetry. Int. Math. Res. Notices 2000(17): 883–908. doi:10.1155/S1073792800000465
  • Conrey, J. B, Snaith, N. C. (2007). Applications of the L-functions ratios conjecture. Proc. London Math. Soc. 94(3): 594–646. doi:10.1112/plms/pdl021
  • Fiorilli, D., Parks, J, Södergren, A. (2018). Low-lying zeros of quadratic Dirichlet L-functions: A transition in the Ratios Conjecture the Ratios Conjecture, Q. J. Math. 69(4): 1129–1149.
  • Hecke, E. (1920). Eine neue Art von Zetafunktionen und ihre Beziehungen zur Verteilung der. Math. Z 6(1-2): 11–51. I., Math. Z. 1 (1918), 357-376. II, Math. Z. doi:10.1007/BF01202991
  • Hejhal, D. (1994). On the triple correlation of zeros of the zeta function. Int. Math. Res. Notices 1994(7): 293–302.
  • Katz, N, Sarnak, P. (1999). Random Matrices, Frobenius Eigenvalues and Monodromy. AMS Colloquium Publications 45. Providence, R.I.: AMS.
  • Katz, N, Sarnak, P. (1999). Zeros of zeta functions and symmetries. Bull. Amer. Math. Soc. 36(01): 1–26. doi:10.1090/S0273-0979-99-00766-1
  • Kubilius, J. (1955). On a problem in the n-dimensional analytic theory of numbers. Vilniaus Valst. Univ. Mokslo Darbai. Mat. Fiz. Chem. Mokslu Ser 4: 5–43.
  • Montgomery, H. (1973). The Pair Correlation of Zeros of the Zeta Function, Analytic number theory, Proc. Sympos. Pure Math., XXIV, Providence, R.I.: American Mathematical Society, pp. 181–193.
  • Odlyzko, A. (1987). On the distribution of spacings between zeros of the zeta function. Math. Comp. 48(177): 273–308. doi:10.1090/S0025-5718-1987-0866115-0
  • Rudnick, Z, Waxman, E. (2019). Angles of Gaussian primes. Isr. J. Math. 232(1): 159–199. doi:10.1007/s11856-019-1867-5
  • Soundararajan, K. (2000). Nonvanishing of quadratic Dirichlet L-functions at s = 1/2. Ann. Math. 152(2): 447–488. doi:10.2307/2661390
  • Waxman, E. Lower order terms for the one level density of a symplectic family of Hecke L-Functions, forthcoming preprint: https://arxiv.org/abs/1905.10362.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.