Both arithmetic aficionados and the mathematically challenged will be equally captivated by new research that upends hundreds of years of popular belief about prime numbers.
Bounds for Dirichlet polynomials play an important role in several questions connected to the distribution of primes. For example, they can be used to bound the number of zeroes of the Riemann zeta function in vertical strips, which is relevant to the distribution of primes in short intervals. A Dirichlet polynomial is a trigonometric polynomial of the form$D(t) = \sum_{n = N}^{2N} b_n n^{it}$
Sine, one of the fundamental trigonometric functions, plays a crucial role in various fields, including mathematics, physics, engineering, and computer science. Its calculation is not trivial, especially when it comes to implementing it in electronic calculators, where efficiency and accuracy are paramount.
An international autumn school "Proof and Computation" will be held from 15th to 21st September 2024 at Aurachhof in Fischbachau near Munich. Its aim is to bring together young researchers in the fields of Foundations of Mathematics, Computer Science and Philosophy.
As a schoolchild, she had delighted in using a pendulum to make drawings in her exercise books, but it was not until midlife that she found in this process a portal to a larger world of ideas. In 1938, using a silver pendulum with a jade end she believed was guided by energy fields — a technique she termed radiesthesia — she began making large-scale drawings in pencil and crayon on graph paper, hundreds of them, to divine diagnoses of physical and psychic ailments and heal people, often with results bordering on the miraculous.
Chez de nombreux végétaux terrestres, les feuilles s’agencent en spirale le long de la tige en suivant une distribution mathématique bien connue. Quand cette structure est-elle apparue ?
K. Ren, und H. Wang. (2023)cite arxiv:2308.08819Comment: 23 pages. v2: fixed small typo in abstract and added more details to arguments, main results unchanged.
M. Escardó. (2019)cite arxiv:1911.00580Comment: 211 pages, extended version of Midlands Graduate School course (2019), includes Agda-verified mathematics. Sources available at github (as explained in the pdf file), but not in LaTeX, last revised September 2022.
M. Porter. (2022)cite arxiv:2201.07794Comment: working paper (associated with my data-ethics lecture at the 2021 AMS Short Course on Mathematical and Computational Methods for Complex Social Systems); not yet refereed; private comments and suggestions are appreciated.
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S. Roberts. Nutrition (Burbank, Los Angeles County, Calif.), 24 (5):
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