Department of Mathematics and Computer Science Number Theory and Combinatorics Seminar Spring 2015 Talks are at noon on Monday in room W565 of University Hall For more information, or to receive an email announcement of each week's seminar, contact Nathan Ng < ng AT cs DOT uleth DOT ca > or Dave Morris .
 The next talk: Jan 26 at noon in UHall W565 Nathan Ng (University of Lethbridge) A subconvexity bound for modular $L$-functions, part 2 This is a continuation of last week's talk. I will sketch Matti Jutila's proof of a subconvex bound for a modular $L$-function on the critical line. The main ideas are an approximate functional equation, the use of Farey fractions, Voronoi's summation formula, and exponential integral and sum estimates.

 Talks in the series this semester: (Click on any title for more info, including the abstract. Then click on it again to hide the info.)

 Date Speaker Title Jan 12 everyone Open problem session at noon in UHall W565 Please bring your favourite (math) problems. Anyone with a problem to share will be given about 5 minutes to present it. We will also choose most of the speakers for the rest of the semester. Jan 19 Nathan Ng A subconvexity bound for modular $L$-functions at noon in UHall W565 Let $L(s)$ be the $L$-function associated to a modular form of weight $k$ for the full modular group. Using spectral theory, Anton Good proved that $L(k/2+it) \ll t^{1/3} (\log t)^{5/6}$. Matti Jutila discovered a simpler proof which makes use of the Voronoi summation formula, exponential integrals, and Farey fractions. We shall present Jutila's argument. Jan 26 Nathan Ng A subconvexity bound for modular $L$-functions, part 2 at noon in UHall W565 This is a continuation of last week's talk. I will sketch Matti Jutila's proof of a subconvex bound for a modular $L$-function on the critical line. The main ideas are an approximate functional equation, the use of Farey fractions, Voronoi's summation formula, and exponential integral and sum estimates. Feb 2 no seminar (PIMS Distinguished Visitor will speak at noon) Feb 9 Speaker TBA Title TBA at noon in UHall W565 Abstract TBA Feb 23 Speaker TBA Title TBA at noon in UHall W565 Abstract TBA Mar 2 Speaker TBA Title TBA at noon in UHall W565 Abstract TBA Mar 9 Farzad Aryan Title TBA at noon in UHall W565 Abstract TBA Mar 16 James Parks Title TBA at noon in UHall W565 Abstract TBA Mar 23 Speaker TBA Title TBA at noon in UHall W565 Abstract TBA Mar 30 Speaker TBA Title TBA at noon in UHall W565 Abstract TBA Apr 13 Robert Craigen Title TBA at noon in UHall W565 (University of Manitoba) Abstract TBA Apr20 Speaker TBA Title TBA at noon in UHall W565 Abstract TBA
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