Thesis (Selection of subject)Thesis (Selection of subject)(version: 285)
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Pretentious approach to analytic number theory
Thesis title in Czech: Předstírající přístup k analytické teorii čísel
Thesis title in English: Pretentious approach to analytic number theory
Key words: analytická teorie čísel, předstírající přístup, aritmetická funkce, rozložení prvočísel
English key words: analytic number theory, pretentious approach, arithmetic function, distribution of prime numbers
Academic year of topic announcement: 2017/2018
Type of assignment: diploma thesis
Thesis language: angličtina
Department: Department of Algebra (32-KA)
Supervisor: Mgr. Vítězslav Kala, Ph.D.
Author: hidden - assigned and confirmed by the Study Dept.
Date of registration: 01.10.2017
Date of assignment: 01.10.2017
Confirmed by Study dept. on: 27.11.2017
Date and time of defence: 14.06.2018 09:00
Date of electronic submission:09.05.2018
Date of submission of printed version:11.05.2018
Date of proceeded defence: 14.06.2018
Reviewers: Mgr. Jaroslav Hančl
 
 
 
Guidelines
The recently developed "pretentious approach" to analytic number theory studies the asymptotic behavior of arithmetic functions using Halasz's theorem from 1975. This allows one to prove a number of important results in analytic number theory without relying on the analytic continuation of the Riemann zeta function. The goal of the thesis is to study and compare the classical and pretentious proofs of such theorems, such as the prime number theorem, Siegel-Walfisz theorem or Halasz theorem, and possibly try to further generalize some of these results.
References
A. Granville, A. J. Harper, K. Soundararajan: A more intuitive proof of a sharp version of Halász's theorem, 2017, arXiv:1706.03755

D. Koukoulopoulos: Pretentious multiplicative functions and the prime number theorem for arithmetic progressions, Compos. Math., 149 (2013), no. 7, 1129-1149

D. Koukoulopoulos: The distribution of prime numbers, online lecture notes, http://dms.umontreal.ca/~koukoulo/documents/notes/primes.pdf
 
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