Some remarks on the convergence of the Dirichlet series of L-functions and related questions

First we show that the abscissae of uniform and absolute convergence of Dirichlet series coincide in the case of $L$-functions from the Selberg class $\mathcal{S}$. We also study the latter abscissa inside the extended Selberg class, indicating a different behavior in the two classes. Next we address two questions about majorants of functions in $\mathcal{S}$, showing links with the distribution of the zeros and with independence results.Comment: 10 page

Ukraine: On the border between old and new in uncertain times

This chapter provides an overview of the demographic situation in Ukraine, including explanations for the decline to very low fertility and changes in family policy. Drawing on official statistics, survey data, and focus group interviews, the analysis shows that the country’s decline to lowest-low fertility is primarily due to the postponement of or the reduction in second births, as opposed to the postponement of first births. The chapter includes a discussion on the link between low fertility and changing marriage patterns, contraceptive prevalence, and abortion. The author then reviews the evidence for the leading explanations of fertility decline in Ukraine, including economic uncertainty, social anomie, the Second Demographic Transition, and unequal gender relations. In addition, the author proposes unexplored factors that may lead to fertility limitation, such as the increasing difficulty of combining work and childrearing, insufficient housing, changes in intergenerational support, and the deterioration of health lifestyles and marital relations.childbearing, fertility, Ukraine

Primes and prime ideals in short intervals

We prove the analog of Cram\'er's short intervals theorem for primes in arithmetic progressions and prime ideals, under the relevant Riemann Hypothesis. Both results are uniform in the data of the underlying structure. Our approach is based mainly on the inertia property of the counting functions of primes and prime ideals.Comment: minor change to Proposition

Harmonized histories: manual for the preparation of comparative fertility and union histories

This document describes the standardization process of the Harmonized Histories. The Harmonized Histories is a comparative database of rich reproductive and union histories from surveys conducted in a number of countries in Europe. Given that birth and union data has been collected in a number of ways in different surveys, it has been very difficult to conduct cross-national analyses of recent union and fertility behavior over time. A team of researchers called the Nonmarital Childbearing Network has cleaned and standardized the surveys according to guidelines set out in this manual. Currently, the database includes data from the Generations and Gender Surveys (GGSs) in Italy, Germany, France, Bulgaria, Hungary, Romania, and Russia; the 2003 Dutch Fertility and Family Survey; and the British Household Panel Survey.Europe, family formation, fertility, surveys