A generalization of Knopp's Observation on Ramanujan's tau-function

被引：2
|
作者：
Pribitkin, Wladimir de Azevedo [1 ,2 ,3 ]
机构：
[1] CUNY, Coll Staten Isl, Dept Math, 2800 Victory Blvd, Staten Isl, NY 10314 USA
[2] Dept Math, Grad Ctr, CUNY, New York, NY 10016 USA
[3] CUNY, Grad Ctr, Dept Math, 365 Fifth Ave, New York, NY 10016 USA
来源：
RAMANUJAN JOURNAL | 2016年 / 41卷 / 1-3期
关键词：
Modular forms; Cusp forms; Fourier coefficients; Nonvanishing; MODULAR INVARIANT J(TAU); PARTITION-FUNCTION P(N); SMALL POSITIVE WEIGHT; FOURIER COEFFICIENTS; AUTOMORPHIC-FORMS; CUSP FORMS; INTEGRALS; SERIES;
D O I：
10.1007/s11139-015-9756-y
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We establish a vast generalization of an observation made by Marvin Knopp half a century ago concerning the nonvanishing of Ramanujan's tau-function.
引用
收藏
页码：519 / 542
页数：24
相关论文
共 50 条
  • [1] A generalization of Knopp’s Observation on Ramanujan’s tau-function
    Wladimir de Azevedo Pribitkin
    The Ramanujan Journal, 2016, 41 : 519 - 542
  • [2] Even values of Ramanujan's tau-function
    Balakrishnan, Jennifer S.
    Ono, Ken
    Tsai, Wei-Lun
    arXiv, 2021,
  • [3] Even Values of Ramanujan’s Tau-Function
    Balakrishnan J.S.
    Ono K.
    Tsai W.-L.
    La Matematica, 2022, 1 (2): : 395 - 403
  • [4] Variations of Lehmer's Conjecture for Ramanujan's tau-function
    Balakrishnan, Jennifer S.
    Craig, William
    Ono, Ken
    JOURNAL OF NUMBER THEORY, 2022, 237 : 3 - 14
  • [5] A FORMULA FOR RAMANUJAN TAU-FUNCTION
    EWELL, JA
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 91 (01) : 37 - 40
  • [6] ODD VALUES OF THE RAMANUJAN TAU-FUNCTION
    MURTY, MR
    MURTY, VK
    SHOREY, TN
    BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 1987, 115 (03): : 391 - 395
  • [7] MULTIPLICATIVE FUNCTIONS AND RAMANUJAN TAU-FUNCTION
    ELLIOTT, PDTA
    JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1981, 30 (APR): : 461 - 468
  • [8] ON ZAGIERS CUSP FORM AND THE RAMANUJAN TAU-FUNCTION
    HASHIM, A
    MURTY, MR
    PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 1994, 104 (01): : 93 - 98
  • [9] AN OMEGA-THEOREM FOR RAMANUJAN TAU-FUNCTION
    BALASUBRAMANIAN, R
    MURTY, MR
    INVENTIONES MATHEMATICAE, 1982, 68 (02) : 241 - 252
  • [10] On Ramanujan's tau function
    Ewell, JA
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1998, 28 (02) : 453 - 461
12345