Peng-Jie Wong

Let K/k be a Galois extension of number fields with Galois group G, and let rho be a non-trivial irreducible representation of G of dimension n. The Artin holomorphy conjecture asserts that the Artin L-function attached to rho extends to an entire...

The study of the asymptotic behaviour of the summatory function of the number of divisors of shifted primes was initiated by Titchmarsh, who used the generalised Riemann hypothesis to establish a main term and remainder for the sum of tau(p-a) for p...

Dirichlet's theorem on arithmetic progressions states that for any (a,q)=1, there are infinitely many primes congruent to a modulo q. Such a theorem together with Euler's earlier work on the infinitude of primes represents the beginning of the study...

Siegel zeros (or Landau-Siegel zeros) are potential counterexamples to the generalised Riemann hypothesis (for L-functions). Such zeros, if exist, have to be "very close" to 1 over the complex plane. In this talk, we will discuss some results...

Bertrand's postulate states that there is always a prime in the interval [x,2x] for any x≥1. Applying the prime number theorem, one may further show that there is approximately ∫2xxdtlogt primes in [x,2x] for sufficiently large x. There is a more...

Let E be a CM elliptic curve defined over the rational numbers. In light of the Lang-Trotter conjecture, there is a question asking for an asymptotic formula for the number of primes p x for which the reduction modulo p of E is cyclic. This has been...