University of Lethbridge

In the 1960s Shanks conjectured that the $\zeta(\rho)$, where $\rho$ is a non-trivial zero of zeta, is both real and positive in the mean. Conjecturing and proving this result has a rich history, but efforts to generalise it to higher moments have so...

The size function h0 for a number field is analogous to the dimension of the Riemann-Roch spaces of divisors on an algebraic curve. Van der Geer and Schoof conjectured that h0 attains its maximum at the trivial class of Arakelov divisors if that...

This talk will begin with a study on explicit bounds for ψ(x) starting with the work of Rosser in 1941. It will also cover various improvements over the years including the works of Rosser and Schoenfeld, Dusart, Faber-Kadiri, Platt-Trudgian, Büthe...

Historically, the notion of Pólya fields dates back to some works of George Pólya and Alexander Ostrowski, in 1919, on entire functions with integer values at integers; a number field $K$ with ring of integers $\mathcal{O}_K$ is called a Pólya field...

The Hardy and Littlewood k-tuple prime conjecture is one of the most enduring unsolved problems in mathematics. In 1999, Gadiyar and Padma presented a heuristic derivation of the 2-tuples conjecture by employing the orthogonality principle of...

Generalizing the original Chebyshev bias can go in many directions: one can adapt the setting to virtually any equidistribution result encoded by a finite number of L-functions. In this talk, we will discuss what happens when one needs an infinite...

Full waveform inversion (FWI) is a novel seismic wave equation-based data-driven approach characterized by exploiting full waveform information from all types of seismic data. It can image the subsurface with high resolution, up to half the...

Let ℤ be the ring of integers, and let 𝔽p[t] be the ring of polynomials in one variable defined over the finite field 𝔽p of p elements. Since the characteristic of ℤ is 0, while that of 𝔽p[t] is the positive prime number p, it is a striking theme in...

In this talk, I will discuss my on-going joint work with Xiannan Li on an unconditional asymptotic formula for the eighth moment of Γ1(q) L-functions, which are associated with eigenforms for the congruence subgroups Γ1(q). Similar to a large family...

The Selberg class consists of functions sharing similar properties to the Riemann zeta function. The Riemann zeta function is one example of the functions in this class. The estimates for logarithms of Selberg class functions and their logarithmic...