Portal de Periódicos da CAPES

The Zeros of Riemann Zeta Partial Sums Yield Solutions to f(x) + f(2x) + · · · + f(nx) = 0

2012; Birkhäuser; Volume: 10; Issue: 3 Linguagem: Inglês

10.1007/s00009-012-0237-x

1660-5454

G. Mora, J. M. Sepulcre,

Advanced Differential Equations and Dynamical Systems

This paper proves that every zero of any n th , n ≥ 2, partial sum of the Riemann zeta function provides a vector space of basic solutions of the functional equation $${f(x) + f(2x) + \cdots + f(nx) = 0, x \in \mathbb{R}}$$ . The continuity of the solutions depends on the sign of the real part of each zero.