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Published March 8, 2026 | Version v1
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Elementary Traversals of 1/(a+b) and the Arithmetic Origin of the Critical Line Symmetry

Description

We prove that the partial sums of 1/(a+b) admit traversals crossing 1/2 iff a=1 and N is odd. The traversal curve connects b*(1)=1/2 to Grandi's series, whose Cesàro sum is 1/2. Via the Specialization Operator, this structure maps onto the critical strip of ζ(s).

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Related works

Is supplemented by
Publication: 10.5281/zenodo.18916005 (DOI)
Publication: 10.5281/zenodo.18932754 (DOI)

References

  • MSC 11M06
  • MSC 11M26
  • MSC 40G05
  • Riemann zeta function
  • critical line
  • Euler product
  • Dirichlet eta function
  • Grandi series
  • Cesàro summation
  • partial sums
  • traversal; geometric series
  • alternating series
  • elementary number theory
  • Szegő theorem
  • lacunary polynomials