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One Level Density for Cubic Galois Number Fields

  • Patrick Meisner (a1)
Abstract

Katz and Sarnak predicted that the one level density of the zeros of a family of L-functions would fall into one of five categories. In this paper, we show that the one level density for L-functions attached to cubic Galois number fields falls into the category associated with unitary matrices.

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The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement no. 320755.

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[1] Bucur, A., Costa, E., David, C., Guerreiro, J., and Lowry-Duda, D., Traces, high powers and one level density for families of curves over finite fields . Math. Proc. Cambridge Philos. Soc. (2017). https://doi.org/10.1017/S030500411700041X.
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[8] Rudnick, Z. and Sarnak, P., Zeros of principal l-functions and random matrix theory . Duke Math. J. 81(1996), no. 2, 269322. https://doi.org/10.1215/S0012-7094-96-08115-6.
[9] Weil, A., Sur les courbes algébriques et les variétés qui s’ en déduisent. Actualités Sci. Ind., 1041, Hermann, Paris,, pp. 1948.
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[11] Yang, A., Distribution problems associated to zeta functions and invariant theory. Ph.D. Thesis, Princeton University, 2009.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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