Undergraduate lectures in Analytic Number Theory
Summer 2009

Room D630, 10:00am - 11:30

Organizers: Habiba Kadiri , Nathan Ng. This summer, the following undergraduate students are doing some research projects in analytic number theory: Laura Faber:.Explicit bounds for the n-th prime number (supervisors: H. Kadiri and N. Ng), Alyssa Lumley: Explicit bounds for some prime counting functions (supervisor: H. Kadiri), Mark Thom: The Riemann zeta function and divisor functions (supervisor: N. Ng). Some talks are given by either the students or the faculty and are related to the subject of their research. Anyone interested is welcome to attend.

Schedule Topic Thursday, May 07 Lecture 1: Arithmetic functions. Alyssa Lumley Friday, May 08 Lecture 2: Partial summations. Mark Thom Friday, May 22 Lecture 3: Tchebycheff's bounds for pi(x). Alyssa Lumley Tuesday, June 02 Lecture 4: Upper bounds for the Riemann Zeta function. Alyssa Lumley Thursday, June 04 Lecture 5: Lower bounds for the Riemann Zeta funtion and non-vanishing on Re s=1. Alyssa Lumley Monday, June 08 Lecture 6: Zero-free region for the Riemann Zeta function. Alyssa Lumley Friday, June 12 Lecture 7: Perron's formula. Nathan Ng Tuesday, June 16 Lecture 8: Explicit formula for the Riemann Zeta function and proof of the Prime Number Theorem. Habiba Kadiri Wednesday, June 17 Lecture 9: Bounds for ζ'/ζ in the strip -1≤ Re s ≤ 2. Habiba Kadiri Tuesday, June 23 Lecture 10: Introduction to the Mellin Transform. David Kaminski Wednesday, July 22 Lecture 11: Explicit formula for a smoothed versino of psi(x). Habiba Kadiri

Participation of the students to the following events: 30 April: Alberta Number Theory Day II, University of Calgary, Alberta. June 05: Colloquium: Mean-value estimates for the Riemann zeta-function. by Micah Milinovich (from University of Mississipi). Slides. June 28-July 18: Undergraduate summer School, Park City, Utah.

Links: Past talks (summer 2008) Number theory in Lethbridge Number theory web