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Showing 1 to 5 of 5 for “"Primes in arithmetic progressions"”.
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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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Quadratic Reciprocity: Proofs and Applications
… of quadratic reciprocity is an important result in number theory. The purpose of this thesis is to present several proofs as well as applications of the law of quadratic reciprocity. I will present three proofs of the quadratic reciprocity. We begin with a proof that depends on Gauss's lemma and …
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Topics in explicit number theory
… of this thesis is as follows. After the introduction, there are four chapters. In Chapters 2 and 3, we obtain explicit bounds for the number of non-trivial zeros of the Riemann zeta function and Dedekind zeta functions, which improve previous results of Trudgian. This improvement is based …
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The distribution of k-free numbers and integers with fixed number of prime factors
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2017-09-29 without embargo terms
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Topics in analytic number theory
This thesis, consisting of two chapters, proves several new theorems concerning L-functions and the distribution of primes. In the first chapter, we establish the first explicit form of the Vinogradov–Korobov zero-free region for Dirichlet L-functions. In the second chapter, we generalize recent …