Fall 2014, UZH: MAT 693.1 Analytic number theory student seminar
Time: Thursday 17:00-19:30
Place: Y27H12, Irchel campus
Email: brad.rodgersmath.uzh.ch, or nicolas.roblesmath.uzh.ch
Course webpage with syllabus: http://www.math.uzh.ch/index.php?ve_se_det&key2=869
Books: There are a large number of books on analytic number theory. Some useful resources include but are not limited to:
It is usually better to pick one book you like and read through it than to try reading through several at the same time (in my experience). A good crash course in complex analysis, if you don't have a background in it, is
- T. Apostol, Introduction to Analytic Number Theory.
- G.H. Hardy and E.M. Wright, Introduction to the Theory of Numbers
- S. J. Miller and R. Takloo-Bighash, An Invitation to Modern Number Theory
- H. Rademacher, Lectures on Elementary Number Theory
- (More advanced) H. Montgomery and R. Vaughan, Multiplicative Number Theory I: Classical Theory
- Chapter 10 and 11 of G. Shilov, Elementary Real and Complex Analysis
A (tentative) calendar of talks. This may be subject to change.
- Sept. 18 - No class
- Sept. 25 - Some fundamentals of number theory (Nicolas)
- Oct. 2 - Some more fundamentals, and arithmetic functions (Nicolas)
- Oct. 9 - Modular arithmetic (Milan)
- Oct. 16 - Quadratic reciprocity (Tania)
- Oct. 23 - Review of complex analysis, and Chebyshev bounds (Brad/Nicolas)
- Oct. 30 - Dirichlet characters (Benjamin)
- Nov. 6 - General Dirichlet Series (Adrienne, 40 min) / Introduction to the Riemann zeta function (Roland, 40 min)
- Nov. 13- Dirichlet's theorem (Andrea 60 min) / Dirichlet's hyperbola trick (Cagla 20 min)
- Nov. 20 - Prime number theorem (Paulo 60 min) / Dirichlet's hyperbola trick (Cagla 20 min)
- Nov. 27 - Twin primes and Brun's constant (Alessandro/Gianluca)
- Dec. 4 - Elliptic curves (Violetta/Dario)
- Dec. 11 - Erdős-Kac theorem (Robert)
- Dec. 18 - Zeros on the critical line: Hardy's theorem (Francesca/Eduardo)
- This class is a pass/fail class.
- Each participant is required to present a talk on a topic of their choice (related to analytic number theory), and hand in a short written version of their talk.
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