Published March 8, 2026
| Version v1
Publication
Open
Elementary Traversals of 1/(a+b) and the Arithmetic Origin of the Critical Line Symmetry
Authors/Creators
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).
Files
pub_traversals.pdf
Files
(299.2 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:29382d66fb079a1f855f2827663dec24
|
299.2 kB | Preview Download |
Additional details
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