Transformations

Shaun Cooper
Additional contact information
Shaun Cooper: Massey University, Institute of Natural and Mathematical Science

Chapter Chapter 2 in Ramanujan's Theta Functions, 2017, pp 129-169 from Springer

Abstract: Abstract Suppose ω 1 and ω 2 are complex numbers that satisfy Im(ω 2∕ω 1) > 0, and let Λ ( ω 1 , ω 2 ) = m ω 1 + n ω 2 : m , n ∈ ℤ . $$\varLambda (\omega _{1},\omega _{2}) = \left \{m\omega _{1} + n\omega _{2}: m,n \in \mathbb{Z}\right \}.$$ We show how properties of Λ(ω 1, ω 2) and certain of its subsets imply transformation formulas for elliptic functions and modular forms. All positive weights can be handled in the same way, and the conditionally convergent cases of weights one and two present no extra difficulty.

Date: 2017
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-56172-1_3

Ordering information: This item can be ordered from
http://www.springer.com/9783319561721

DOI: 10.1007/978-3-319-56172-1_3

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().