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Showing 1 to 8 of 8 for “"Prime Number Theorem"”.
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The prime number theorem: Analytic and elementary proofs
Three proofs of the prime number theorem are presented. The �rst is a heavily analytic proof based on early accounts. Cauchy's residue theorem and various results relating to the Riemann zeta function play a vital role. A weaker result than the prime number theorem is used for the proof, namely …
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A Detailed Proof of the Prime Number Theorem for Arithmetic Progressions
… that J. Elstrodt published in 1998 to prove the Prime Number Theorem for arithmetic progressions. We will review basic results from Dirichlet characters and L-functions. Furthermore, we establish a weak version of the Wiener-Ikehara Tauberian Theorem, which is an essential tool for the proof of …
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On the Theory of Zeta-functions and L-functions
… formulations and approaches to the proof of the Prime Number Theorem and the Riemann Hypothesis. These two topics constitute the main theme of this thesis. For the Prime Number Theorem, we provide a thorough discussion that compares and contrasts Norbert Wiener's proof with that of Newman's short …
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Explicit Estimates for Functions of Primes in Arithmetic Progressions
… numerical estimates for the error term in the prime number theorem for arithmetic progressions, and Waring's problem for cubes.
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On Beurling's Theory of Generalized Numbers
… 255-291), we consider a set of generalized prime numbers $P=\{1<p\sb1\le p\sb2\le\...\}$ and the set of generalized integers $N=\{n\sb1=1\le n\sb2\le\...\}$ generated by P. We let $N(x)$ be the counting function of the set N. In this thesis we give continuous versions of generalized number …
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Vergleichende multiplikative Zahlentheorie
Unter der Annahme der verallgemeinerten Riemannschen Vermutung beweise ich eine effektive Variante des Satzes von Littlewood, partielle Ergebnisse zum Shanks-Renyi-race-Problem sowie Aussagen ueber lokale Schwankungen in der Primzahlverteilung. Als Hilfsmittel fuehre ich einen neuen Begriff von …
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Complexity in physical, living and mathematical systems
… we present a stochastic algorithm that generates primes. An algorithmic phase transition takes place distinguishing the ability of the algorithm to generate primes. Both Monte Carlo simulations and analytical developments are provided in order to characterize the dynamics of the system and explain …