5 papers
Galois-Orbit Structure, Ramanujan Sums, and Stable-Range Collapse for Cyclotomic Cosine Formulas
Juan D. Vélez, Carlos A. Cadavid
We study cyclotomic cosine evaluations beyond the fully symmetric setting by combining Galois-orbit structure with finite-frequency expansions. First, for truncation-compatible pol…
Eventual Morse Minimality of Heat Flow on Lens Spaces
Carlos A. Cadavid, Dairo J. Hernández, Juan Diego Vélez
We prove that heat flow generically produces Morse-minimal functions on round lens spaces. The result gives a rigorous explanation of a phenomenon first suggested by computational…
Spectral Selection and Minimal Morse Structures on the Poincaré Dodecahedral Space
Carlos A. Cadavid, Juan D. Velez, Sergio Lenis
We study the long time behavior of the heat equation on the spherical Poincare dodecahedral space and introduce a spectral selection property P, asserting that for a dense open set…
Inverse-Limit Formulas and Stable-Range Rigidity for Cyclotomic Sums
Juan D. Velez, Carlos Cadavid
We study truncation compatible families F = (F_m)_{m>=1} over Q[z] through an inverse limit formalism, and we evaluate them at the punctured cyclotomic cosine points alpha_{k,n} =…
Hurwitz complete sets of factorizations in the modular group and the classification of Lefschetz elliptc fibrations over the disk
J. D. Vélez, C. Cadavid, L. Moreno
Given any matrix B in SL(2,Z), we will describe an algorithm that provides at least one elliptic fibration over the disk, relatively minimal and Lefschetz, within each topological…