Fourth Bucharest Number Theory Day, July 19, 2016

Organizers: Alina Cojocaru, Vicentiu Pasol, Alexandru Popa

This year, the conference is dedicated to the 150th anniversary of the Romanian Academy. The workshop is partially supported by CNCSIS grant TE-2014-4-2077.

The talks will take place at IMAR in Amfiteatrul "Miron Nicolescu" (parter). No registration is necessary.

Invited speakers

Schedule of talks

  9:30-10:20   Alexandru Buium
Towards a differential geometry of the integers
10:20-10:40   Coffee break
10:40-11:30   Florin Boca
Statistics of Farey fractions and the distribution of eigenvalues in large sieve matrices
11:40-12:30   Titus Hilberdink
Singular values of multiplicative Toeplitz matrices

12:30-14:30   Lunch break

14:30-15:20   Nathan Jones
Never-primitive points on elliptic curves over the rationals
Abstract: Artin's primitive root conjecture states that, given an integer c that is neither equal to -1 nor a perfect square, there are infinitely many primes p for which c is a primitive root modulo p. In the 1970s Lang and Trotter formulated an analogue for an elliptic curve E over the rational numbers: given a rational point Q on E of infinite order, they conjectured a precise density for the number of primes p for which the reduction of Q mod p generates the entire group of Z/pZ-rational points of E. In this talk we will discuss the following question: under what conditions on E and Q is the predicted density in Lang-Trotter's generalization of Artin's primitive root conjecture equal to zero? (In such a case we call Q a "never-primitive" point on E.) This represents ongoing joint work with F. Pappalardi and P. Stevenhagen.
15:20-15:40   Coffee break
15:40-16:30   Alina Cojocaru
Reductions of elliptic curves over function fields of positive characteristic