Automorphic L-functions lie at the confluence of number theory, harmonic analysis and representation theory. These functions generalise the classical Riemann zeta function and are constructed from ...

The section introduces notation and outlines the proof for establishing lower bounds of Dirichlet L-functions by relating these bounds to the distribution of zeros, leveraging results from prominent ...

R. P. Conceic˜ao, C. Hall & D. Ulmer, “Explicit points on the Legendre curve II”, Math. Res. Lett. 21 (2014), no. 2, p. 261-280. C. Davis & T. Occhipinti ...

There was a lot of excitement last month about ‘L-functions’. A PhD student in the Department of Mathematics, Ce Bian, in collaboration with his supervisor, Dr Andrew Booker, had discovered some new ...

Abstract: We study the value-distribution of Dirichlet L-functions L(s, χ) in the half-plane σ = ℜ s>1/2. The main result is that a certain average related to the logarithm of L(s, χ) with respect to ...

This section proves Proposition 2.2, establishing key properties of zeros for L(s, ψ)L(s, χψ) in the domain Ω using various lemmas and integrative techniques. In this section we prove Proposition 2.2.

Structure functions relate the level of operations of a system as a function of the level of the operation of its components. In this paper structure functions are studied which have an intuitive ...