Theta Functions

Emil Grosswald
Additional contact information
Emil Grosswald: Temple University, College of Liberal Arts

Chapter Chapter 8 in Representations of Integers as Sums of Squares, 1985, pp 91-106 from Springer

Abstract: Abstract We recall from Chapter 1 that the determination of r k (n) can be reduced to that of the coefficient a n (k) in the Taylor series expansion of the function $$ {\left( {\sum\nolimits_{{m = - \infty }}^{\infty } {{x^{{{m^2}}}}} } \right)^k} = {\left( {1 + 2\sum\nolimits_{{m = 1}}^{\infty } {{x^{{{m^2}}}}} } \right)^k} $$ , because this series, denoted traditionally by |θ3(x)} k , equals $$ \sum\nolimits_{{ - \infty

Keywords: Entire Function; Periodic Function; Elliptic Function; Theta Function; Taylor Series Expansion (search for similar items in EconPapers)
Date: 1985
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:978-1-4613-8566-0_9

Ordering information: This item can be ordered from
http://www.springer.com/9781461385660

DOI: 10.1007/978-1-4613-8566-0_9

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 ().