Representations of certain binary quadratic forms as a sum of Lambert series and eta-quotients

被引:2
|
作者
Ye, Dongxi [1 ]
机构
[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA
关键词
Binary quadratic forms; eta-quotients; Lambert series; PRODUCTS;
D O I
10.1142/S1793042115500578
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this work, we establish formulas for the representations of binary quadratic forms of discriminants -44, -92, -108, -135 and -140 as a sum of Lambert series and etaquotients.
引用
收藏
页码:1073 / 1088
页数:16
相关论文
共 50 条
  • [11] Ternary Quadratic Forms and Eta Quotients
    Williams, Kenneth S.
    CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2015, 58 (04): : 858 - 868
  • [12] Certain eta-quotients and arithmetic density of Andrews' singular overpartitions
    Singh, Ajit
    Barman, Rupam
    JOURNAL OF NUMBER THEORY, 2021, 229 : 487 - 498
  • [13] Certain eta-quotients and ℓ-regular partitions with distinct odd parts
    Ray, Chiranjit
    RAMANUJAN JOURNAL, 2024,
  • [14] Representations of binary forms by certain quinary positive integral quadratic forms
    Kim, MH
    Koo, JK
    Oh, BK
    JOURNAL OF NUMBER THEORY, 2001, 89 (01) : 97 - 113
  • [15] Representations of integers by certain positive definite binary quadratic forms
    Murty, M. Ram
    Osburn, Robert
    RAMANUJAN JOURNAL, 2007, 14 (03): : 351 - 359
  • [16] Representations of integers by certain positive definite binary quadratic forms
    M. Ram Murty
    Robert Osburn
    The Ramanujan Journal, 2007, 14 : 351 - 359
  • [17] On the number of representations of a positive integer as a sum of two binary quadratic forms
    Alaca, Saban
    Pehlivan, Lerna
    Williams, Kenneth S.
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2014, 10 (06) : 1395 - 1420
  • [18] Parity of the coefficients of certain eta-quotients, II: The case of even-regular partitions
    Keith, William J.
    Zanello, Fabrizio
    JOURNAL OF NUMBER THEORY, 2023, 251 : 84 - 101
  • [19] Binary quadratic forms and the eta function
    Chapman, R
    van der Poorten, AJ
    NUMBER THEORY FOR THE MILLENNIUM I, 2002, : 215 - 227
  • [20] ON THE REPRESENTATIONS OF INTEGERS BY CERTAIN QUADRATIC FORMS
    Xia, Ernest X. W.
    Yao, Olivia X. M.
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2013, 9 (01) : 189 - 204