Zeros of Dirichlet L-functions on the critical line with the accuracy of 40000 decimal places

The zeros of Dirichlet L-functions for various moduli and characters are being computed with very high accuracy on a cluster of workstations at Deakin University. This collection is growing to include more zeros (other moduli and characters).

Digital shimmer: popular music and the intimate nexus between fan and star

Conception of ‘star performance’ through popular music is stratified which generates diverse and often contradictory forms of thought. For example, stars and celebrities plausibly act as a ‘culture medium’ in which, through imagination, one’s identity is assembled, realised or constructed. What to become and how to be are questions we individually and collectively contend with throughout our lives to varying degrees (Maslow, 1954; 1968). Predominant use of digital technologies has seen the delivery of sound much altered. Music, be it Giuseppe Verdi’s La Traviata or Iron Maiden’s The Number of the Beast, once sourced via analogue legacy devices such as ‘old-school’ tape cassette or vinyl record is now a series of zero and one digits. Advocates argue that the key benefit of digitalisation is the ability to compress data because sound generates large files of information. The discourse of digitalisation begs the question of how a series of ones and zeros, albeit in a plethora of configurations, registers with listening bodies and affects ‘the sublime’. It is without doubt that some musical experiences afford indescribable, unlocatable sensation—even enchantment (as defined by Bennett, 2001: 5 and called forth by Redmond: 2014: 126). Such musical experiences might be in the presence of the performer or in their absence such as in the case of recorded music. In this context, any sense of ’real’ space and place is less definitive allowing for ‘special encounters’ to be imagined and felt. For these reasons, music and all that the use of the word might convey, the proposed notion of phaino-ken here, acts as the lens through which to examine the meaning and value of celebrity and star embodiment.

Approximation of riemanns zeta function by finite dirichlet series: A multiprecision numerical approach

The finite Dirichlet series of the title are defined by the condition that they vanish at as many initial zeros of the zeta function as possible. It turns out that such series can produce extremely good approximations to the values of Riemanns zeta function inside the critical strip. In addition, the coefficients of these series have remarkable number-theoretical properties discovered in large-scale high-precision numerical experiments. So far, we have found no theoretical explanation for the observed phenomena.