Weber Functions and Weierstrass Sigma Function Associated with Hecke Operators
International Conference of Numerical Analysis and Applied Mathematics (ICNAAM), Kos, Greece, 19 - 25 September 2012, vol.1479, pp.356-359, (Full Text)
- Publication Type: Conference Paper / Full Text
- Volume: 1479
- Doi Number: 10.1063/1.4756137
- City: Kos
- Country: Greece
- Page Numbers: pp.356-359
- Keywords: Dedekind eta function, Hecke operators, Weber functions, Weierstrass sigma-function
- Akdeniz University Affiliated: No
Abstract
In this paper we investigate the action of the Hecke operators to families of Weber functions and the Weierstrass sigma-function. We prove that the function of -eta(2)/8 + logs sigma (1/2, tau) is an eigenfunction (or eigenform) of the Hecke operator where eta(2) is a variable depending on tau in definition of Weierstrass sigma-function.