Explicit Estimates in the Theory of Prime Numbers
It is the purpose of this thesis to enunciate and prove a collection of explicit results in the theory of prime numbers. First, the problem of primes in short intervals is considered. We furnish an explicit result on the existence of primes between consecutive cubes. To prove this, we first derive an explicit version of the Riemann--von Mangoldt explicit formula. We then assume the Riemann hypothesis and improve on the known conditional explicit...[Show more]
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