On Additive Divisor Sums and Partial Divisor Functions

We establish asymptotic formulae for various correlations involving general divisor functions $d_k(n)$ and partial divisor functions $d_l(n,A)=\sum_{q|n:q\leq n^A}d_{l-1}(q)$, where $A\in[0,1]$ is a parameter and $k,l\in\mathbb{N}$ are fixed. Our results relate the parameter $A$ to the lengths of arithmetic progressions in which $d_k(n)$ is uniformly distributed. As applications to additive divisor sums, we establish new lower bounds and a new equivalent condition for the conjectured asymptotic. We also prove a Tauberian theorem for general additive divisor sums.Comment: 28 page

Mean Value Theorems for L-functions over Prime Polynomials for the Rational Function Field

The first and second moments are established for the family of quadratic Dirichlet $L$--functions over the rational function field at the central point $s=\tfrac{1}{2}$ where the character $\chi$ is defined by the Legendre symbol for polynomials over finite fields and runs over all monic irreducible polynomials $P$ of a given odd degree. Asymptotic formulae are derived for fixed finite fields when the degree of $P$ is large. The first moment obtained here is the function field analogue of a result due to Jutila in the number--field setting. The approach is based on classical analytical methods and relies on the use of the analogue of the approximate functional equation for these $L$--functions.Comment: 17 page

ENACTING LEVINAS’S INFINITE RESPONSIBILITY AS AN ETHICO-POLITICAL COMPROMISE

A obra de Lévinas não nos oferece uma teoria ética, antes procura descrever um encontro ético pré-originário com o outro. Neste encontro face a face com o outro, a minha subjectividade torna-se refém por causa de uma assimetria original entre nós. Esta assimetria ética produz uma responsabilidade infinita pelo e para o outro, de modo a que a singularidade do outro possa ser preservada. Para moderar uma posição tão exigente como esta, Lévinas introduz um terceiro que restaura a justiça ao permitir o cálculo ético. Isto assinala uma passagem da ética para a política. Ainda assim, permanece uma lacuna entre ética e política. Defendo uma leitura da pretensão de Lévinas segundo a qual o terceiro ´r uma correcção correcção da assimetria de proximidade de modo a afirmar a responsabilidade infinita como o compromisso da ética com a política. Discuto algumas implicações para a ética dos negócios, em particular CSR, à luz destas descobertas.Levinas’s work does not offer us an ethical theory but seeks rather to describe a pre-originary ethical encounter with the other. Within this face-to-face encounter with the other, my subjectivity is held hostage because of an originary asymmetry between us. This ethical asymmetry produces an infinite responsibility to and for the other, in order that the singularity of the other be preserved. In order to moderate such a demanding position Levinas introduces the third party who restores justice by permitting ethical calculation. This marks a move from ethics to politics. Nonetheless, there remains a lacuna between ethics and politics. I argue for a reading of Levinas’s claim that the third party is an incessant correction of the asymmetry of proximity in order to posit infinite responsibility as the compromise of ethics with politics. I discuss some implications for business ethics, in particular CSR, in light of these findings