Sum of divisors in a ring of gaussian integers

被引：0
|
作者：
Sinyavskii O.V. [1 ]
机构：
[1] Odessa University, Odessa
来源：
Ukrainian Mathematical Journal | 2001年 / 53卷 / 7期
关键词：
Asymptotic Formula; Arithmetic Progression; Narrow Sector; Gaussian Integer;
D O I：
10.1023/A:1013333400370
中图分类号：
学科分类号：
摘要：
We construct an asymptotic formula for a sum function for σa(α), where σa(α) is the sum of the ath powers of the norms of divisors of the Gaussian integer a on an arithmetic progression α = α0 (mod γ) and in a narrow sector (φ1 ≤ arg α < φ2- For this purpose, we use a representation of σa(n) in the form of a series in the Ramanujan sums. © 2001 Plenum Publishing Corporation.
引用
收藏
页码：1156 / 1170
页数：14
相关论文
共 50 条
  • [31] SUPPLEMENT TO COMPUTING AN ARITHMETIC CONSTANT RELATED TO THE RING OF GAUSSIAN INTEGERS
    GRAMAIN, F
    WEBER, M
    MATHEMATICS OF COMPUTATION, 1985, 44 (169) : S13 - S16
  • [32] The cubic mapping graph for the ring of Gaussian integers modulo n
    Wei, Yangjiang
    Nan, Jizhu
    Tang, Gaohua
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2011, 61 (04) : 1023 - 1036
  • [33] ON DIVISORS OF SUMS OF INTEGERS .5.
    SARKOZY, A
    STEWART, CL
    PACIFIC JOURNAL OF MATHEMATICS, 1994, 166 (02) : 373 - 384
  • [34] ON DIVISORS OF SUMS OF INTEGERS .2.
    SARKOZY, A
    STEWART, CL
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1986, 365 : 171 - 191
  • [35] ON DIVISORS OF SUMS OF INTEGERS .1.
    SARKOZY, A
    STEWART, CL
    ACTA MATHEMATICA HUNGARICA, 1986, 48 (1-2) : 147 - 154
  • [36] COMPLEX SUM OF DIVISORS
    SPIRA, R
    AMERICAN MATHEMATICAL MONTHLY, 1961, 68 (02): : 120 - &
  • [37] DIVISORS OF INTEGERS IN ARITHMETIC-PROGRESSION
    VARBANEC, PD
    ZARZYCKI, P
    CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1990, 33 (02): : 129 - 134
  • [38] The distribution law of divisors on a sequence of integers
    Mohamed Saber Daoud
    Afef Hidri
    Mongi Naimi
    Lithuanian Mathematical Journal, 2015, 55 : 474 - 488
  • [39] SUM OF DIVISORS OF AN INTEGER
    BAGER, A
    RUSS, S
    AMERICAN MATHEMATICAL MONTHLY, 1967, 74 (09): : 1143 - &
  • [40] RECURRENCES FOR SUM OF DIVISORS
    EWELL, JA
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 64 (02) : 214 - 218
12345