# 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

**Florin Boca**, University of Illinois at Urbana-Champaign
**Alexandru Buium**, University of New Mexico
**Alina Cojocaru**, University of Illinois at Chicago and IMAR
**Titus Hilberdink**, University of Reading
**Nathan Jones**, University of Illinois at Chicago

## 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*