Workshop on Recent Trends in Analytic Number Theory

10 am - 11 Peter Sarnak, IAS/Princeton University
"L-Functions and Equidistribution"

11:10 - 12:10 Philippe Michel, IAS/Université Montpellier II, FranceÂ
"Rankin-Selberg L Functions in the Level Aspect"

12:10 - 2 LUNCH, Institute Dining Hall

2 - 3 Kannan Soundararajan, IAS/Princeton University
"Real Zeros of Quadratic Dirichlet L-Functions."

3 - 3:30 REFRESHMENT BREAK, Fuld Hall Common Room

3:30 - 4:30 Jean Bourgain, Institute for Advanced Study
"On Large Values Estimates for Dirichlet Sums and the
Density Hypothesis for the Zeta Function."
 

Thursday, April 13

11:10 - 12:10 William Duke, Rutgers University
"The Splitting of Primes in Division Fields of Elliptic Curves."

12:10 - 2 LUNCH, Institute Dining Hall

2 - 3 Fernando Rodriguez-Villegas, University of Texas - Austin
"Distributuion of Sha of Twists"

3 - 3:30 REFRESHMENT BREAK, Fuld Hall Common Room

3:30 - 4:30 Ken Ono, Penn State University
"Tate-Shafarevich Groups and Ranks of Quadratic Twists of
Elliptic Curves."

4:30 - 5:30 Joseph Silverman, Brown University
"Canonical Heights on Elliptic Curves: An Analytic Perspective."

Friday, April 14

10 am - 11 Andrew Granville, University of Georgia

11:10 - 12:10& D. Roger Heath-Brown, Oxford University
"Counting Rational Points on Curves and Surfaces."

12:10 - 2 LUNCH, Institute Dining Hall

2 - 3 Dennis Hejhal, IAS/Uppsala Univ./Univ. of Minnesota.

3 - 3:30 REFRESHMENT BREAK, Fuld Hall Common Room

3:30 - 4:30
"Explicit Formulas for Mean Values of a Class of Zeta-Functions."

4:30 - 5:30 Fernando Chamizo, Universidad Autonoma de Madrid
"The Hyperbolic Circle Problem and its Applications."

Saturday, April 15

10 am - 11
"On Degree Conjecture in the Selberg Class."

11:10 - 12:10 Alberto Perelli, IAS/University of Genova, Italy
"The Selberg Class: Invariants and Rigidity."

12:10 - LUNCH, Institute Dining Hall
Workshop concludes

Stimulated by the currect activity and in partnership with the Clay Mathematics Institute, we concluded the program with a workshop on Recent Trends in Analytic Number Theory held at the Insitute during April 12 - 15, 2000.

The main objective of this workshop was to present the best (old and new) achievements in the described subjects, as well as to expand interactions between various specialists.