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Using a smoothing function and recent knowledge on the zeros of the Riemann zeta-function, we compute pairs of (∆, x 0 ) such that for all x ≥ x 0 there exists at least one prime in the interval (x(1 − ∆ −1 ), x].

We establish an improved lower bound for a weighted counting function of representations of n as the sum of a prime and a square-free number and provide several applications for this bound. These applications are generalisations of a result of Dudek [4], which states that every natural number greater than 2 may be written as the sum of a prime and a square-free number.

Time-Dependent Dielectric Breakdown Under AC Stress in GaN MIS-HEMTsThe MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters.

No abstract