A central limit theorem for Ramanujan’s tau function

被引：0
作者：
P. D. T. A. Elliott
机构：
[1] University of Colorado at Boulder,Department of Mathematics
来源：
The Ramanujan Journal | 2012年 / 29卷
关键词：
Ramanujan tau function; Modular function; Central limit theorem; 11F11; 11F30; 11N60; 11N36; 11N37;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A central limit theorem is established for the absolute value of the modular Fourier-coefficient function defined by Ramanujan, and for that of the error term in the formula counting representations of integers as sums of twenty-four squares, in which the function appears.
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页码：145 / 161
页数：16
相关论文
共 20 条
  • [1] Barnet–Lamb T.(2011)A family of Calabi–Yau varieties and potential automorphy, II Publ. Res. Inst. Math. Sci. 47 29-98
  • [2] Geraghty D.(1974)La conjecture de Weil, I Inst. Ht. Études Sci. Publ. Math. 43 273-307
  • [3] Harris M.(1981)Multiplicative functions and Ramanujan’s J. Aust. Math. Soc. 30 461-468
  • [4] Taylor R.(1987)-function Bull. Lond. Math. Soc. 19 522-530
  • [5] Deligne P.(1984)The norms of compositions of arithmetic operators Math. Ann. 266 507-511
  • [6] Elliott P.D.T.A.(1917)On the absolute value of Ramanujan’s Proc. Camb. Philos. Soc. 19 117-124
  • [7] Elliott P.D.T.A.(1983)-function Math. Ann. 266 233-239
  • [8] Elliott P.D.T.A.(1987)On Mr. Ramanujan’s empirical expressions of modular functions Bull. Soc. Math. Fr. 115 391-395
  • [9] Moreno C.(1916)The fourth moment of Ramanujan Trans. Camb. Philos. Soc. 22 159-184
  • [10] Shahidi F.(1939)-function Proc. Camb. Philos. Soc. 35 357-373
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