On the values of certain q-hypergeometric series II

被引：0
|
作者：
Amou, M [1 ]
Katsurada, M [1 ]
Väänänen, K [1 ]
机构：
[1] Gunma Univ, Dept Math, Kiryu, Gumma 3768515, Japan
来源：
ANALYTIC NUMBER THEORY | 2002年 / 6卷
关键词：
Irrationality; Irrationality measure; q-hypergeometric series; q-Bessel function; S-unit equation;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
As a continuation of the previous work by the authors having the same title, we study the arithmetical nature of the values of certain q-hypergeometric series phi(z; q) with a rational or an imaginary quadratic integer q with \q\ > 1, which is related to a g-analogue of the Bessel function J(0)(z). The main result determines the pairs (q, alpha) with alpha is an element of K for which phi(alpha; q) belongs to K, where K is an imaginary quadratic number field including q.
引用
收藏
页码：17 / 25
页数：9
相关论文
共 50 条
  • [21] Q-HYPERGEOMETRIC GAUSS EQUATION AND ITS SOLUTIONS AS SERIES AND INTEGRALS
    GELFAND, IM
    GRAEV, MI
    RETAKH, VS
    DOKLADY AKADEMII NAUK, 1993, 331 (02) : 140 - 143
  • [22] SOME TRANSFORMATIONS AND REDUCTION FORMULAS FOR MULTIPLE Q-HYPERGEOMETRIC SERIES
    SRIVASTAVA, HM
    ANNALI DI MATEMATICA PURA ED APPLICATA, 1986, 144 : 49 - 56
  • [23] Variants of q-Hypergeometric Equation
    Hatano, Naoya
    Matsunawa, Ryuya
    Sato, Tomoki
    Takemura, Kouichi
    FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA, 2022, 65 (02): : 159 - 190
  • [24] SOME TRANSFORMATION FORMULAS OF q-HYPERGEOMETRIC SERIES VIA CONTOUR INTEGRATION
    Au, Kam Cheong
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 149 (10) : 4159 - 4170
  • [25] MULTIPLICATIVE q-HYPERGEOMETRIC SERIES ARISING FROM REAL QUADRATIC FIELDS
    Bringmann, Kathrin
    Kane, Ben
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 363 (04) : 2191 - 2209
  • [26] Partial theta functions and mock modular forms as q-hypergeometric series
    Kathrin Bringmann
    Amanda Folsom
    Robert C. Rhoades
    The Ramanujan Journal, 2012, 29 : 295 - 310
  • [27] Recursion formulas for Srivastava's general triple q-hypergeometric series
    Verma, Ashish
    Yadav, Sarasvati
    AFRIKA MATEMATIKA, 2020, 31 (5-6) : 869 - 885
  • [28] Recursion formulas for Srivastava’s general triple q-hypergeometric series
    Ashish Verma
    Sarasvati Yadav
    Afrika Matematika, 2020, 31 : 869 - 885
  • [29] Partial theta functions and mock modular forms as q-hypergeometric series
    Bringmann, Kathrin
    Folsom, Amanda
    Rhoades, Robert C.
    RAMANUJAN JOURNAL, 2012, 29 (1-3): : 295 - 310
  • [30] Quasi -Orthogonality of Some Hypergeometric and q-Hypergeometric Polynomials
    Tcheutia, Daniel D.
    Jooste, Alta S.
    Koepf, Wolfram
    SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2018, 14
12345