Conformal maps and critical points of Eisenstein series

Key Points

• Critical points are identified where associated polymorphic functions have poles, enhancing our understanding of these forms.
• The explicit description of polymorphic functions as conformal maps aids in analyzing the critical points of E_2, E_4, and E_6.
• This research provides insights into how conformal maps can qualitatively describe locations of critical points effectively.
• Understanding these critical points may lead to more significant applications in number theory and complex analysis.