Spring 2025 - MATH 843 G100
Analytic and Diophantine Number Theory (4)
Class Number: 2758
Delivery Method: In Person
Overview
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Course Times + Location:
Jan 6 – Apr 9, 2025: Wed, Fri, 2:30–4:20 p.m.
Burnaby
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Instructor:
Nils Bruin
nbruin@sfu.ca
1 778 782-3794
Description
CALENDAR DESCRIPTION:
Arithmetical functions, distribution of prime numbers, theory of Dirichlet characters, Dirichlet series, theory of Riemann Zeta functions and Dirichlet L-functions, exponential sums, character sums, Diophantine equations, Diophantine approximations, applications.
COURSE DETAILS:
This course provides an introduction into analytic number theoretic methods with applications to arithmetic geometry. We will study Dirichlet series with applications to distributions of prime numbers and as examples of L-series. We will also look at modular forms and their applications to the arithmetic of elliptic curves and their moduli spaces.
We will also consider results in diophantine approximation, such as lower bounds on linear combinations of logs of algebraic numbers, with as application Siegel's theorem on finiteness of integral points on elliptic curves.
Grading
- Biweekly assignments (weighted equally) 30%
- Presentation 15%
- Final Examination (take home) 55%
REQUIREMENTS:
- Undergraduate algebra (groups, rings, fields); Galois theory recommended
- Undergraduate complex analysis
Materials
REQUIRED READING:
T. Apostol, Introduction to Analytic Number Theory, UTM,
Springer-Verlag, 1st ed. 1976. Corr. 5th printing 1998 Edition.
ISBN: 0387272267
F. Diamond, J. Shurman, A First Course in Modular Forms, Graduate Texts
in Mathematics Volume 228, Springer, 2006.
ISBN: 9780387272269
REQUIRED READING NOTES:
Your personalized Course Material list, including digital and physical textbooks, are available through the SFU Bookstore website by simply entering your Computing ID at: shop.sfu.ca/course-materials/my-personalized-course-materials.
Graduate Studies Notes:
Important dates and deadlines for graduate students are found here: http://www.sfu.ca/dean-gradstudies/current/important_dates/guidelines.html. The deadline to drop a course with a 100% refund is the end of week 2. The deadline to drop with no notation on your transcript is the end of week 3.
Registrar Notes:
ACADEMIC INTEGRITY: YOUR WORK, YOUR SUCCESS
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Each student is responsible for his or her conduct as it affects the university community. Academic dishonesty, in whatever form, is ultimately destructive of the values of the university. Furthermore, it is unfair and discouraging to the majority of students who pursue their studies honestly. Scholarly integrity is required of all members of the university. http://www.sfu.ca/policies/gazette/student/s10-01.html
RELIGIOUS ACCOMMODATION
Students with a faith background who may need accommodations during the term are encouraged to assess their needs as soon as possible and review the Multifaith religious accommodations website. The page outlines ways they begin working toward an accommodation and ensure solutions can be reached in a timely fashion.