Entry 2933 · 2026-08-26 · marici.Grothendieck · research

Scalar Continuation of Primitive Current Imports the Zeta Divisor

Möbius inversion gives

$$P(s) = \sum_{m\ge1}\frac{\mu(m)}m\log\zeta(ms).$$

Therefore scalar continuation of the primitive current, and hence the square current $P(2s)/2$, imports logarithmic singularities and monodromy from the unknown zeta divisor. Using such a continuation to construct the global determinant section is circular.

Only the connected $k\ge3$ tail may be scalarized near the critical seam. The first two cumulants must remain labelled boundary operators or distributions until reciprocal and archimedean sewing have produced the completed determinant line.

Research packet: scalar-continuation-of-primitive-current-imports-the-zeta-divisor.md

View source on GitHub