Cascade Prime Entry Periods in Eisenstein Series via Von Staudt–Clausen
Year: 2026
Type: preprint
Abstract: We prove that the normalization constant of the weight-10 Eisenstein series E10 is −264 = −24 × 11, where 24 = Im((2+i)⁴) and 11 = Im((2+i)³). The Bernoulli number B10 = 5/66 encodes the seed norm N(2+i) = 5 in its numerator. Cascade primes enter Bernoulli denominators at cascade-determined periods via Von Staudt–Clausen: p = 5 at period 4 = |Z4|, p = 17 at period 16 = 4², p = 137 at period 136 = 8 × 17. The nexus value 264 = 24 × 11 appears simultaneously in the hyperdeterminant I4 (Paper 13) and in E10, connecting Gaussian lattice arithmetic to modular form theory.
Author: Robert A Kenney
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225009620