arXiv subjects

M. Righetti

Publications and source records attributed to M. Righetti.

2 recordsLinked to original sources

arXiv2019

The converse of Bohr's equivalence theorem with Fourier exponents linearly independent over the rational numbers

Given two arbitrary almost periodic functions with associated Fourier exponents which are linearly independent over the rational numbers, we prove that the existence of a common open vertical strip $V$, where both functions assume the same set of values on every open vertical substrip included in $V$, is a necessary and sufficient condition for both functions to have the same region of almost periodicity and to be $^*$-equivalent or Bohr-equivalent. This result represents the converse of Bohr's equivalence theorem for this particular case.

math.CA↗

arXiv2017

A rigidity theorem for translates of uniformly convergent Dirichlet series

It is well known that the Riemann zeta function, as well as several other $L$-functions, is universal in the strip $1/2<σ<1$; this is certainly not true for $σ>1$. Answering a question of Bombieri and Ghosh, we give a simple characterization of the analytic functions approximable by translates of $L$-functions in the half-plane of absolute convergence. Actually, this is a special case of a general rigidity theorem for translates of Dirichlet series in the half-plane of uniform convergence. Our results are closely related to Bohr's equivalence theorem.

math.NT↗