Results 31 to 40 of about 11,421,197 (96)
Finite saturation for unirational varieties [PDF]
, 2017 We import ideas from geometry to settle Sarnak's saturation problem for a large class of algebraic ...
Sofos, Efthymios, Wang, Yuchao
core +3 more sources
Analyzing the effects of economic sanctions: Recent theory, data, and quantification
Review of International Economics, Volume 32, Issue 1, Page 1-11, February 2024.Abstract Inspired by the increased interest in economic sanctions and their consequences, this special issue contains a collection of studies by experts aiming to reflect the recent developments and trends in the literature on economic sanctions. The contributions contain theoretical research on the topic, data collection, and empirical work on the ...
Peter Egger +2 more
wiley +1 more source
On pairs of equations with unequal powers of primes and powers of 2
AIMS MathematicsIt is proved that every pair of sufficiently large even integers can be represented in the form of a pair of equations, each containing two squares of primes, two cubes of primes, two biquadrates of primes, and $ 30 $ powers of 2.
Li Zhu
doaj +1 more source
Exceptional sets in Waring's problem: two squares and s biquadrates [PDF]
, 2014 Let $R_s(n)$ denote the number of representations of the positive number $n$ as the sum of two squares and $s$ biquadrates. When $s=3$ or $4$, it is established that the anticipated asymptotic formula for $R_s(n)$ holds for all $n\le X$ with at most $O(X^
Zhao, Lilu
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An Invitation to Additive Prime Number Theory [PDF]
, 2005 2000 Mathematics Subject Classification: 11D75, 11D85, 11L20, 11N05, 11N35, 11N36, 11P05, 11P32, 11P55.The main purpose of this survey is to introduce the inexperienced reader to additive prime number theory and some related branches of analytic number ...
Kumchev, A., Tolev, D.
core
Sums of four squares of primes
, 2015 Let $E(N)$ denote the number of positive integers $n \le N$, with $n \equiv 4 \pmod{24}$, which cannot be represented as the sum of four squares of primes. We establish that $E(N)\ll N^{11/32}$, thus improving on an earlier result of Harman and the first
Kumchev, Angel V., Zhao, Lilu
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Sums of four prime cubes in short intervals
, 2018 We prove that a suitable asymptotic formula for the average number of representations of integers $n=p_{1}^{3}+p_{2}^{3}+p_{3}^{3}+p_{4}^{3}$, where $p_1,p_2,p_3,p_4$ are prime numbers, holds in intervals shorter than the the ones previously known ...
Languasco, Alessandro +1 more
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What is the smallest prime? [PDF]
, 2012 What is the first prime? It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers.
Caldwell, Chris K., Xiong, Yeng
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Sums of two squares and a power
, 2016 We extend results of Jagy and Kaplansky and the present authors and show that for all $k\geq 3$ there are infinitely many positive integers $n$, which cannot be written as $x^2+y^2+z^k=n$ for positive integers $x,y,z$, where for $k\not\equiv 0 \bmod 4$ a
C. Hooley +10 more
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Mean values of Dirichlet polynomials and applications to linear equations with prime variables
, 2004 We prove a new mean-value theorem for Dirichlet polynomials with coefficients given by the von Mangoldt function. We then use our theorem to derive new estimates for certain exponential sums over primes.
Angel V. Kumchev +2 more
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