Conformal maps and critical points of Eisenstein series

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This is a Quantitative Study study.

Mario Bonk

doi:10.48550/arxiv.2506.21471

June 26, 2025Open Access

Conformal maps and critical points of Eisenstein series

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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.

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Implication

This investigation reveals critical points of quasi-modular forms E_2, E_4, and E_6, suggesting implications for their associated polymorphic functions.

Abstract

We investigate the critical points of the basic (quasi-)modular forms E₂, E₄, and E₆. They occur where some associated polymorphic functions have poles. By an explicit description of these polymorphic functions as conformal maps, one can give an accurate qualitative analysis of the locations of the critical points of E₂, E₄, and E₆.

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Cite This Study

Mario Bonk (2025) studied this question.

synapsesocial.com/papers/68f04acce559138a1a06e964 https://doi.org/10.48550/arxiv.2506.21471

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Conformal maps and critical points of Eisenstein series

Key Points

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Implication

Abstract

Discussion

Cite This Study

Conformal maps and critical points of Eisenstein series

Key Points

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Implication

Abstract

Discussion

Cite This Study

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