Exact Formula for the Prime Boundary Error in the Gauss Circle Problem
Puntos clave
To derive a closed-form expression for the boundary error related to prime numbers in lattice point counting.
Analysis of the (s,t)-decomposition of counting functions.
Mathematical derivation of closed-form expressions for error terms.
A precise formula for the boundary error e(s,x) when s is prime is established.
Insights into the behavior of the lattice point counting function under prime conditions.
Resumen
We derive a closed-form expression for the per-s boundary error e(s,x) when s is prime, in the (s,t)-decomposition of the primitive lattice point counting function.