An Eisenstein series of rational weight
Xiao-Jie Zhu

TL;DR
This paper investigates a specific Eisenstein series of rational weight, establishing its modularity and deriving its Fourier expansion, thereby expanding understanding of modular forms with fractional weights and complex multiplier systems.
Contribution
It proves the modularity of a rational weight Eisenstein series with a complex multiplier system and explicitly computes its Fourier expansion.
Findings
Confirmed the Eisenstein series is a modular form.
Derived explicit Fourier expansion of the series.
Enhanced understanding of rational weight modular forms.
Abstract
We study an Eisenstein series of weight , level whose multiplier system is the same as . We prove that it is a modular form and obtain its Fourier expansion.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Mathematical Identities · Analytic Number Theory Research
