Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 1206.11055
Farkas, Hershel M.
Theta functions in complex analysis and number theory. (English)
[A] Alladi, Krishnaswami (ed.), Surveys in number theory. New York, NY: Springer. Developments in Mathematics 17, 57-87 (2008). ISBN 978-0-387-78509-7/hbk

Summary: In these notes we try to demonstrate the utility of the theory of theta functions in combinatorial number theory and complex analysis. The main idea is to use identities among theta functions to deduce either useful number-theoretic information related to representations as sums of squares and triangular numbers, statements concerning congruences, or statements concerning partitions of sets of integers. In complex analysis the main utility is in the theory of compact Riemann surfaces, with which we do not deal. We do show how identities among theta functions yield proofs of Picard's theorem and a conformal map of the rectangle onto the disk.

MSC 2000:: *11F27 Theta series; Weil representation
11B65 Binomial coefficients, etc.
30C20 Conformal mappings of special domains
33E05 Elliptic functions and integrals

Keywords: theta functions; triangular numbers; partitions; Riemann map; Picard's theorem

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]