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Abstract Let E k ( z ) be the normalized Eisenstein series of weight k for the modular group SL ( 2 , Z ) . We study the zeros… Click to show full abstract
Abstract Let E k ( z ) be the normalized Eisenstein series of weight k for the modular group SL ( 2 , Z ) . We study the zeros of E k to prove that the equation ∏ i = 1 n E k i = ∏ j = 1 m E l j has no solutions, except for those given by known relationships between E 4 , E 6 , E 8 , E 10 , and E 14 . We go on to discuss some implications of this result.
Keywords:
series;
eisenstein series;
monomials eisenstein
Journal Title: Journal of Number Theory
Year Published: 2021
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Journal Title: Journal of Number Theory
Year Published: 2021
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!