Warianty tytułu
Abstrakty
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.
$∑_{{(a,b,x,y) ∈ ℕ ⁴ \atop ax+by=n}} (F(a-b) - F(a+b))$,
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.
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
445
Liczba stron
72
Liczba rozdzia³ów
Opis fizyczny
Daty
wydano
2007
Twórcy
autor
- Centre for Research in Algebra and Number Theory, School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
autor
- Centre for Research in Algebra and Number Theory, School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
autor
- Centre for Research in Algebra and Number Theory, School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
autor
- Centre for Research in Algebra and Number Theory, School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Bibliografia
Języki publikacji
EN |
Uwagi
Identyfikator YADDA
bwmeta1.element.bwnjournal-rm-doi-10_4064-dm445-0-1
Identyfikatory
DOI
10.4064/dm445-0-1
Kolekcja
DML-PL
