Lambert series and Liouville's identities

A. Alaca, et al. Lambert series and Liouville's identities. 2007. <http://eudml.org/doc/285958>.

@book{A2007,
abstract = {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 $∑_\{\{(a,b,x,y) ∈ ℕ ⁴ \atop ax+by=n\}\} (F(a-b) - F(a+b))$, where n ∈ ℕ and F: ℤ → ℂ is an even function, is equivalent to the Lambert series for $(∑_\{n=1\}^\{∞\} (qⁿ/(1-qⁿ))sin nθ)²$ (θ ∈ ℝ, |q| < 1) given by Ramanujan.},
author = {A. Alaca, Ş. Alaca, E. McAfee, K. S. Williams},
keywords = {Lambert series; Liouville identities; Ramanujan},
language = {eng},
title = {Lambert series and Liouville's identities},
url = {http://eudml.org/doc/285958},
year = {2007},
}

TY - BOOK
AU - A. Alaca
AU - Ş. Alaca
AU - E. McAfee
AU - K. S. Williams
TI - Lambert series and Liouville's identities
PY - 2007
AB - 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 $∑_{{(a,b,x,y) ∈ ℕ ⁴ \atop ax+by=n}} (F(a-b) - F(a+b))$, where n ∈ ℕ and F: ℤ → ℂ is an even function, is equivalent to the Lambert series for $(∑_{n=1}^{∞} (qⁿ/(1-qⁿ))sin nθ)²$ (θ ∈ ℝ, |q| < 1) given by Ramanujan.
LA - eng
KW - Lambert series; Liouville identities; Ramanujan
UR - http://eudml.org/doc/285958
ER -