Factorizations of Eisenstein Series of Level up to 4
Henri Cohen

TL;DR
This paper reveals new factorizations of classical Eisenstein series and theta functions, expressing them as products of conjugate Eisenstein series of half their weight and double their level, with identities across levels 2, 3, and 4.
Contribution
It introduces novel factorizations of Eisenstein series and theta functions into products of conjugate series, extending understanding of their structure across multiple levels.
Findings
E_4( au) factors into conjugate Eisenstein series
2E_2(2τ)-E_2(τ) factors similarly
Identities for E_6 and levels 2, 3, 4
Abstract
We show that the most standard Eisenstein series such as or , and also the function , are in a natural way the product of two conjugate Eisenstein series of half their weight and double their level, as well as a number of similar elementary identities for and Eisenstein series of levels , , and .
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Algebra and Geometry · Analytic Number Theory Research
