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Research ArticleOpen accessOn the Elliptic Function Arising from the Theta Functions and Dedekind's η-FunctionIsmet Yildiz, Neslihan UyanikIt's a reality that there is a relationship between the sigma function of Weierstrass and theta functions. An elliptic function can be set up using the theta functions just as it can be astablished with the help of sigma function of Weierstrass and two relations between the Dedekind's h-function and - theta function were established by the using characteristic values … …Journal of Mathematics and Statistics, Vol. 1, Issue 2 · 30 Jun 2005 · 6,367 accessesView PDFCite
Research ArticleOpen accessOn the Relations among Characteristic Functions of Theta FunctionsIsmet Yildiz, Neslihan UyanikIn this study, using the characteristic values $\begin{bmatrix} \varepsilon\\ \varepsilon' \end{bmatrix} = \begin{bmatrix} 1\\ 1 \end{bmatrix}, \begin{bmatrix} 1\\ 0 \end{bmatrix}, \begin{bmatrix} 0\\ 1 \end{bmatrix}, \begin{bmatrix} 0\\ 0 \end{bmatrix} \pmod 2$ a theorem on the $\frac{1}{2^r}$ coefficients of periods of first order theta function according to the $(1,τ)$ period pair (for $r \in N^+$) is established. The following equalities are also … …Journal of Mathematics and Statistics, Vol. 1, Issue 2 · 30 Jun 2005 · 6,044 accessesView PDFCite