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Revisiting the Gross–Zagier discriminant formula
Author(s) -
Ye Dongxi
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900298
Subject(s) - discriminant , mathematics , linear discriminant analysis , invariant (physics) , pure mathematics , prime (order theory) , quadratic equation , combinatorics , statistics , mathematical physics , artificial intelligence , geometry , computer science
We derive a formula for the discriminant of the ring class polynomial of conductor N associated to the j ‐invariant and an imaginary quadratic field of odd discriminant − d using the theory of Borcherds lifts. When d is a prime and N = 1 , the formula recovers the Gross–Zagier discriminant formula.
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