1,047 research outputs found
The power-saving Manin-Peyre conjectures for a senary cubic
No full textUsing recent work of the first author [S. Bettin, High moments of the Estermann function. Algebra Number Theory 47(3) (2018), 59–684], we prove a strong version of the Manin-Peyre's conjectures with a full asymptotic and a power-saving error term for the two varieties respectively in with bihomogeneous coordinates and in with multihomogeneous coordinates defined by the same equation . We thus improve on recent work of Blomer et al [The Manin–Peyre conjecture for a certain biprojective cubic threefold. Math. Ann. 370 (2018), 491–553] and provide a different proof based on a descent on the universal torsor of the conjectures in the case of a del Pezzo surface of degree 6 with singularity type and three lines (the other existing proof relying on harmonic analysis by Chambert-Loir and Tschinkel [On the distribution of points of bounded height on equivariant compactifications of vector groups. Invent. Math. 148 (2002), 421–452]). Together with Blomer et al [On a certain senary cubic form. Proc. Lond. Math. Soc. 108 (2014), 911–964] or with work of the second author [K. Destagnol, La conjecture de Manin pour une famille de variétés en dimension supérieure. Math. Proc. Cambridge Philos. Soc. 166(3) (2019), 433–486], this settles the study of the Manin–Peyre conjectures for this equation
A congruence sum and rational approximations
No full textWe give a reciprocity formula for a two-variables sum where the variables satisfy a linear congruence condition. We also prove that such sum is a measure of how well a rational is approximable from below and show that the reciprocity formula is a simple consequence of this fact
Health spending in Italy: The impact of immigrants
No full textThe welfare impact of immigration is a highly debated issue especially for countries on the external borders of the European Union. This paper studies how immigrants affect public health expenditure across Italian regions during the period 2003–2016 using NUTS II level data. Identification strategy is based on shift–share instruments, which are made robust to pull factors that might attract immigrants in Italy and to internal migration of natives. We find that a 1 percentage point increase in immigrants over total resident population leads to a decrease in public health expenditure per capita by about 3.8% (i.e. around 69 euro per capita). Among possible channels, we find no support for any crowding out effect from public to private health services by natives due to increasing immigration or for any role played by different levels of efficiency across regional health systems. Our results are driven by immigrants' demographic structure: they are mostly males and younger workers that call for less health spending, according to a positive selection mechanism. Moreover, linguistic barriers contribute to limiting the immigrants' reliance on public healthcare, which is confirmed also by the use of the European Health Interview Survey microdata
ON THE DISTRIBUTION OF A COTANGENT SUM
No full textAbstract. Maier and Rassias computed the moments and proved a distribution re-sult for the cotangent sum c0(a/q): = − m<
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