Singular part of the arithmetic Siegel–Weil formula

Formulate precisely and prove the singular (degenerate) part of the arithmetic Siegel–Weil formula for unitary Shimura varieties, including determining the constant term that should relate the arithmetic volume of the Shimura variety to logarithmic derivatives of Dirichlet L-functions, and establish a complete identity between arithmetic degrees (including singular terms) and modified central derivatives of Eisenstein series.

Background

The paper proves an arithmetic Siegel–Weil formula for nonsingular terms, expressing arithmetic degrees of intersections of special cycles in terms of modified central derivatives of incoherent Eisenstein series, including corrections from bad reduction. However, the singular part (including constant and degenerate Fourier coefficients) is not yet formulated or proved. The author notes that even the constant term should match arithmetic volumes with logarithmic derivatives of Dirichlet L-functions; some related volume formulas have been obtained, but a complete singular-term correspondence is missing.