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math.NT2025
Single-valued periods of meromorphic modular forms and a motivic interpretation of the Gross-Zagier conjecture
Francis Brown, Tiago J. Fonseca
A well-known conjecture of Gross and Zagier states that the values of the higher automorphic Green's function at pairs of points with complex multiplication in the upper half-plane…
math.AG2025
Positive geometries and canonical forms via mixed Hodge theory
Francis Brown, Clément Dupont
''Positive geometries'' are a class of semi-algebraic domains which admit a unique ''canonical form'': a logarithmic form whose residues match the boundary structure of the domain.…