Lambert series and Liouville's identities

被引:3
作者
Alaca, A. [1 ]
Alaca, S. [1 ]
McAfee, E. [1 ]
Williams, K. S. [1 ]
机构
[1] Carleton Univ, Sch Math & Stat, Ctr Res Algebra & Number Theory, Ottawa, ON K1S 5B6, Canada
关键词
Liouville's identities; lambert series; Ramanujan's identity;
D O I
10.4064/dm445-0-1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The relationship between Liouville's arithmetic identities and products of Lambert series is investigated. For example it is shown that Liouville's arithmetic formula for the sum Sigma (F(a - b) - F(a + b)), (a,b,x,y)epsilon N-4 ax+by=n where n epsilon N and F : Z -> C is an even function, is equivalent to the Lambert series for (Sigma(infinity)(n=1) 1 - q(n)/q(n) sin n theta)(2) (theta epsilon R, |q| < 1) given by Ramanujan.
引用
收藏
页码:5 / 72
页数:68
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