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Analytic Number Theory

Master's level | 7.5 credits | Course code: MMA340

The course does not start as a freestanding course this academic year but can start within a program or a course package. Please contact the department for further information.

About the Course

Analytic number theory is the part of number theory that uses methods from analysis to answer questions about integers in general and prime numbers in particular. The subject became an independent part of number theory during the 19th century, when works by Dirichlet and Riemann, among others, showed that methods from complex analysis could be used to study the distribution of primes among the natural numbers. Riemann only wrote one ten-page paper in analytic number theory, but his ideas have permeated much of the research in the field during the last 150 years. Riemann's fundamental insight was that the distribution of primes is intimately connected to a complex function called the Riemann zeta function. This function has since been thoroughly studied, not least in connection with the so-called Riemann hypothesis which describes the location of the zeroes of the zeta function.

In this course you will study arithmetic functions, Dirichlet series, the Riemann zeta function, and Dirichlet L functions. We will use this to prove the prime number theorem and the prime number theorem for arithmetic progressions, which in various ways describe the distribution of primes among the natural numbers.

More Information

http://www.chalmers.se/sv/in...

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Course Syllabus

MMA340

Tuition Fee

Please contact the department.
EU/EEA citizens, Swedish residence permit holders and exchange students do not pay fees. More information on: http://www.universityadmissions.se

Study Guidance

svl.math@gu.se, tel: 031-772 3505

Department

Department of Mathematical Sciences
41296 Göteborg

Visiting address: Chalmers Tvärgata 3

Phone: 0317721000

Page Manager: Pontus Sundén
Last update: 6/15/2018 12:12 PM

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Page Manager: Pontus Sundén|Last update: 10/16/2018
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Denna text är utskriven från följande webbsida:
http://utbildning.gu.se/education/courses-and-programmes/course_detail/?courseid=MMA340
Utskriftsdatum: 2019-11-18