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pro vyhledávání: '"Duker A"'
We study solutions to the equation $a+b=c$, where $a,b,c$ form a triple of coprime natural numbers. The $abc$ conjecture asserts that, for any $\epsilon>0$, such triples satisfy $\mathrm{rad}(abc) \ge c^{1-\epsilon}$ with finitely many exceptions. In
Externí odkaz:
http://arxiv.org/abs/2410.12234
We obtain density theorems for cuspidal automorphic representations of $\text{GL}_n$ over $\mathbb{Q}$ which fail the generalized Ramanujan conjecture at some place. We depart from previous approaches based on Kuznetsov-type trace formulae, and inste
Externí odkaz:
http://arxiv.org/abs/2408.13682
Autor:
Duker Annelieke E.C., Karimba Benson Mutuma, Wani Grace E., Prasad Pooja, Van der Zaag Pieter, De Fraiture Charlotte
Publikováno v:
Cahiers Agricultures, Vol 31, p 7 (2022)
In the semi-arid lands of southern Kenya, a dynamic process of farmer-led irrigation has developed over the past two decades. It is characterised by short-term agreements to access land and water. Resident and migrant farmers, capital providers and l
Externí odkaz:
https://doaj.org/article/de710fb80ec445ba9cf095a582ff979b
In this expository note, we give a concise and accessible introduction to the real-analytic determinant method for counting integral points on algebraic curves, based on the classic 1989 paper of Bombieri-Pila.
Comment: 17 pages. arXiv admin not
Comment: 17 pages. arXiv admin not
Externí odkaz:
http://arxiv.org/abs/2312.12890
Autor:
Lichtman, Jared Duker
We show the primes have level of distribution $66/107\approx 0.617$ using triply well-factorable weights. This gives the highest level of distribution for primes in any setting, improving on the prior record level $3/5=0.60$ of Maynard. We also exten
Externí odkaz:
http://arxiv.org/abs/2309.08522
In 1935, Erd\H{o}s proved that the sums $f_k=\sum_n 1/(n\log n)$, over integers $n$ with exactly $k$ prime factors, are bounded by an absolute constant, and in 1993 Zhang proved that $f_k$ is maximized by the prime sum $f_1=\sum_p 1/(p\log p)$. Accor
Externí odkaz:
http://arxiv.org/abs/2303.08277
For $k\ge1$, let $R_k(x)$ denote the reciprocal sum up to $x$ of numbers with $k$ prime factors, counted with multiplicity. In prior work, the authors obtained estimates for $R_k(x)$, extending Mertens' second theorem, as well as a finer-scale estima
Externí odkaz:
http://arxiv.org/abs/2303.06481
Autor:
Lichtman, Jared Duker
We prove the infinitude of shifted primes $p-1$ without prime factors above $p^{0.2844}$. This refines $p^{0.2961}$ from Baker and Harman in 1998. Consequently, we obtain an improved lower bound on the the distribution of Carmichael numbers. Our main
Externí odkaz:
http://arxiv.org/abs/2211.09641
Autor:
Pooja Prasad, Annelieke Duker, Diego Zuluaga Velasquez, Moline Chauruka, Benson M. Karimba, Charlotte de Fraiture, Emmanuel Manzungu, Pieter van der Zaag
Publikováno v:
Frontiers in Water, Vol 6 (2024)
Conventional approaches to irrigation development involve large lumpsum investments in big infrastructure that cannot adapt to changing climate and socio-economic conditions. There is an urgent need for alternative ways of investing in smallholder ir
Externí odkaz:
https://doaj.org/article/a514a2916ed045c4b845d0b3b66605c0
Publikováno v:
PeerJ, Vol 12, p e17471 (2024)
The restoration of succulent thicket (the semi-arid components of the Albany Subtropical Thicket biome endemic to South Africa) has largely focused on the reintroduction of Portulacaria afra L. Jacq—a leaf- and stem-succulent shrub—through the pl
Externí odkaz:
https://doaj.org/article/77e1916d6e414de1913c50e4174707f3