On the monotonicity of the ratio of some hyperelliptic integrals of order 7

被引：3
|
作者：
Bakhshalizadeh, A. [1 ]
Asheghi, R. [1 ]
Kazemi, R. [2 ]
机构：
[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran
[2] Univ Kashan, Fac Math, Kashan 8731753153, Iran
来源：
BULLETIN DES SCIENCES MATHEMATIQUES | 2020年 / 158卷
关键词：
Monotonicity; Hyperelliptic integrals; Algebraic criteria; Hamiltonian function; CRITERION;
D O I：
10.1016/j.bulsci.2019.102810
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the monotonicity of the ratio of some hyperelliptic integrals of order 7. These integrals are related to the 1-forms ydx, xydx and defined by the hyperelliptic curves of dH = 0, with H(x,y) = y(2) + P-7(x), where P-7 is a polynomial of degree 7 depending on three parameters alpha, beta and gamma. Our results are based on the well-known algebraic criteria. (C) 2019 Elsevier Masson SAS. All rights reserved.
引用
收藏
页数：24
相关论文
共 50 条
  • [1] The monotonicity of the ratio of hyperelliptic integrals
    Wang, Na
    Xiao, Dongmei
    Yu, Jiang
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2014, 138 (07): : 805 - 845
  • [2] MONOTONICITY OF THE RATIO OF TWO ABELIAN INTEGRALS FOR A CLASS OF SYMMETRIC HYPERELLIPTIC HAMILTONIAN SYSTEMS
    Kazemi, Rasool
    [J]. JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2018, 8 (01): : 344 - 355
  • [3] The monotonicity of the ratio of two hyperelliptic Abelian integrals for a class of symmetric potential systems of degree eight
    Mohammad, G.
    Asheghi, R.
    Kazemi, R.
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2022, 176
  • [4] THE MONOTONICITY OF THE RATIO OF TWO ABELIAN INTEGRALS
    Liu, Changjian
    Xiao, Dongmei
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2013, 365 (10) : 5525 - 5544
  • [5] The monotonicity of ratios of some Abelian integrals
    Sun, Xianbo
    Wang, Na
    Yu, Pei
    [J]. BULLETIN DES SCIENCES MATHEMATIQUES, 2021, 166
  • [6] On some hyperelliptic Hurwitz-Hodge integrals
    Lewanski, Danilo
    [J]. MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 2023, 175 (02) : 271 - 284
  • [7] Zeros of hyperelliptic integrals of the first kind for special hyperelliptic Hamiltonians of degree 7
    Bakhshalizadeh, A.
    Asheghi, R.
    Hoseyni, R.
    [J]. CHAOS SOLITONS & FRACTALS, 2017, 103 : 279 - 288
  • [8] The hyperelliptic integrals and π
    Scarpello, Giovanni Mingari
    Ritelli, Daniele
    [J]. JOURNAL OF NUMBER THEORY, 2009, 129 (12) : 3094 - 3108
  • [9] Criterion for determining the monotonicity of the ratio of two Abelian integrals
    Li, CZ
    Zhang, ZF
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 124 (02) : 407 - 424
  • [10] New criteria for the monotonicity of the ratio of two Abelian integrals
    Liu, Changjian
    Chen, Guoting
    Sun, Zhongqin
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 465 (01) : 220 - 234
12345