Summer School — Inclusive Paths in Explicit Number Theory

How primes and L-functions are linked is at the core of analytic number theory, with the Gener- alized Riemann Hypothesis (GRH) being its star conjecture. The field of explicit number theory focuses on simple yet notoriously difficult questions such as the Goldbach conjecture (Can every even number be written as the sum of two primes?) and Legendre’s conjecture (Is there a prime number between every two consecutive squares?). It is likely one of the most exacting flavors of number theory: in addition to scientific creativity, it requires precision and endurance to produce meaningful results. Working in teams with complementary expertise would allow to tackle some problems in the field more efficiently.