1,355,565 research outputs found
The exceptional set for the number of primes in short intervals
No full textAbstractWe investigate the exceptional set Eδ(X, h) associated with the asymptotic formula for the number of primes in short intervals; see Section 1 for the definition. We first obtain two results about the basic structure of this set, proving the inertia and decrease properties; see Theorem 1. Then we turn to estimates for the size of Eδ(X, h), showing that non-trivial bounds for |Eδ(X, h)| can be obtained when h(x)=xθ and 1/6<θ<7/12; see Theorem 2
Analytic Number Theory
No full textLectures given by J. B. Friedlander, D. R. Heath-Brown, H. Iwaniec, J. Kaczorowski at a C.I.M.E. Summer School held in Cetraro, Italy. Editors: A. Perelli and C. Viola. Springer Lecture Notes in Mathematics vol. 1891
Goldbach numbers represented by polynomials
No full textLet N be a large positive real number. It is well known that almost all even integers in the interval [N, 2N] are Goldbach numbers, i.e. a sum of two primes. The same result also holds for short intervals of the form [N, N+H], see Mikawa [4], Perelli-Pintz [7] and Kaczorowski-Perelli-Pintz [3] for the choice of admissible values of H and the size of the exceptional set in several problems in this direction. One may ask if similar results hold for thinner sequences of integers in [N, 2N], of cardinality smaller than the upper bound for the exceptional set in the above problems. In this paper we deal with the polynomial case
Spatial aspects of the rise of nonmarital fertility across Europe since 1960: the role of states and regions in shaping patterns of change
No full textThis article investigates the role of states and regions in shaping spatial patterns of nonmarital fertility in Europe since 1960 using a dataset of 497 European subnational regions and smaller countries. Almost all regions registered substantial nonmarital fertility increases over the last 50 years. Prior research has shown that in the first half of the twentieth century states played a dominant role in drawing the demographic map of Europe (Watkins, From provinces into nations: demographic integration in Western Europe 1870–1960. Princeton University Press, Princeton, 1991). As a result, subnational regional variation decreased, while differences between countries increased. In this article, we investigate whether states continue to play such a dominant role in delineating patterns of nonmarital fertility between 1960 and 2007. We find that variation in nonmarital fertility levels increased as a whole across Europe, and states continued to be important for determining these patterns. However, the role of states relative to regions declined in the latest period examined (1990 and 2007). Possible explanations for the changes include increased supranational integration, for example, within the European Union, and decentralisation within states leading to increases in variation in subnational contextual conditions.RésuméCet article étudie le rôle des États et des régions dans l’élaboration des modèles spatiaux de fécondité hors mariage en Europe depuis 1960 à l’aide d’un ensemble de données de 497 régions infranationales et petits pays européens. Presque toutes les régions ont enregistré de substantielles augmentations de fécondité hors mariage au cours des 50 dernières années. Une précédente recherche a montré qu’au cours de la première moitié du 20ème siècle, les États ont joué un rôle prédominant dans l’établissement de la carte démographique de l’Europe (Watkins, From provinces into nations: demographic integration in Western Europe 1870–1960. Princeton University Press, Princeton, 1991). En conséquence, la variation infranationale régionale a diminué tandis que les différences entre les pays ont augmenté. Dans cet artiche, nous examinons dans quelle mesure les États continuent à jouer ce rôle prédominant dans la définition des modèles de fécondité hors mariage entre 1960 et 2007. Nous constatons que les niveaux de fécondité hors mariage ont augmenté dans l’ensemble de l’Europe et que les États continuent à jouer un rôle important dans la détermination de ces modèles. Toutefois, le rôle des États par rapport aux régions a diminué au cours de la dernière période étudiée (1990 et 2007). Les explications possibles des changements incluent la croissance de l’intégration supranationale, par exemple au sein de l’Union Européenne, et la décentralisation au sein des États, engendrant une augmentation de la variabilité des conditions contextuelles infranationales
The Generations and Gender Survey Wave 1
No full textThe author has stored the data on an external site "UK Data Service". We have validated this Pure record so that the metadata for the dataset will be visible on Eprints.
Perelli-Harris, B., Maslovskaya, O., Berrington, A. (2024). United Kingdom Generations and Gender Survey, 2022-2023: Special Licence Access. [data collection]. UK Data Service. SN: 9247, DOI: http://doi.org/10.5255/UKDA-SN-9247-1</span
On the average order of multiplicative functions
No full textIn questo lavoro si generalizza un teorema di G. Halàss riguardante le medie di funzione aritmetiche moltiplicativ
Ukraine: On the border between old and new in uncertain times
No full textThis 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
A spectral universality theorem for Maass L-functions
No full textWe show that for a positive proportion of Laplace eigenvalues ,
the associated Hecke-Maass -functions approximate with
arbitrary precision any target function on a closed disc with center
in and radius r<1/4.
The main ingredients in the proof are the spectral large sieve of
Deshouillers-Iwaniec and Sarnak's equidistribution theorem for Hecke eigenvalues
L-functions of degree 2 and conductor 1: underlying ideas and a generalisation
No full textWe present a streamlined account of a recent theorem on the classification of the -functions of degree 2 and conductor 1 from the extended Selberg class. We also present a more general new result dealing with functional equations involving two Dirichlet series. Further, we correct a slip in the original proof of the above theorem, which however does not affect the final result
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