A Riemann–von Mangoldt-Type Formula for the Distribution of Beurling Primes

In this paper we work out a Riemann–von Mangoldt type formula for the summatory function := , where is an arithmetical semigroup (a Beurling generalized system of integers) and is the corresponding von Mangoldt function attaining with a prime element and zero otherwise. On the way towards this formula, we prove explicit estimates on the Beurling zeta function , belonging to , to the number of zeroes of in various regions, in particular within the critical strip where the analytic continuation exists, and to the magnitude of the logarithmic derivative of , under the sole additional assumption that Knopfmacher’s Axiom A is satisfied. We also construct a technically useful broken line contour to which the technic of integral transformation can be well applied. The whole work serves as a first step towards a further study of the distribution of zeros of the Beurling zeta function, providing appropriate zero density and zero clustering estimates, to be presented in the continuation of this paper.

THE USE OF ONE-LINE MODEL AND LITTORAL DRIFT ROSE CONCEPT IN PREDICTING LONG TERM EVOLUTION OF THE MOLISE COAST

The long term evolution of the Molise coast (South-East Italy) is analyzed using the Littoral Drift Rose (LDR) concept, coupled to the GENESIS numerical model, which is based on the one line contour equation. LDR has been used to define a single, climate-equivalent, time-invariant sea state, which has been supposed to entirely rule the shoreline changes. Particular attention has been drawn to a 5 km long reach of coast, just south to the mouth of the Trigno river. Results of the analysis indicate the adopted procedure, even if extremely simplified, can explain nearly 90percent of the observed shoreline trend.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/1g0gRCVkaW4