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Titlebook: Computational Excursions in Analysis and Number Theory; Peter Borwein Book 2002 Springer Science+Business Media New York 2002 Diophantine

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41#
發(fā)表于 2025-3-28 17:29:32 | 只看該作者
42#
發(fā)表于 2025-3-28 19:54:38 | 只看該作者
43#
發(fā)表于 2025-3-28 23:54:43 | 只看該作者
,The Erd?s—Szekeres Problem,st the sum of the absolute values of the coefficients of the polynomial . when it is expanded, and an ideal solution of the Prouhet-Tarry-Escott problem arises when .. = 2. (as in Theorem 1(c) of Chapter 11).
44#
發(fā)表于 2025-3-29 05:25:30 | 只看該作者
LLL and PSLQ,y of our applications LLL can be treated as a “black box”—why it works doesn’t matter. One inputs a lattice and receives as output a candidate short vector that can be verified to have the requisite properties for the particular problem under consideration.
45#
發(fā)表于 2025-3-29 08:42:43 | 只看該作者
46#
發(fā)表于 2025-3-29 14:13:36 | 只看該作者
Book 2002face of analysis and number theory. Some of these problems are the following: The Integer Chebyshev Problem. Find a nonzero polynomial of degree n with integer eoeffieients that has smallest possible supremum norm on the unit interval. Littlewood‘s Problem. Find a polynomial of degree n with eoeffie
47#
發(fā)表于 2025-3-29 19:05:51 | 只看該作者
https://doi.org/10.1007/978-3-8349-9310-6y of our applications LLL can be treated as a “black box”—why it works doesn’t matter. One inputs a lattice and receives as output a candidate short vector that can be verified to have the requisite properties for the particular problem under consideration.
48#
發(fā)表于 2025-3-29 22:11:23 | 只看該作者
,Die F?rderstiftung als Organisation,e constant . depends only on . and . This suggests the question of establishing the exact value for . Specifically, we search for the minimum positive value in the spectrum of height . polynomials evaluated at a number ., where . is between 1 and 2.
49#
發(fā)表于 2025-3-30 00:44:59 | 只看該作者
Die Stiftungslandschaft in Deutschland,roblem is .. So to date, the “easier” Waring problem is not easier than the Waring problem. However, the best bounds for small . are derived in an elementary manner from solutions to the Prouhet-Tarry-Escott problem. This is discussed later in this chapter.
50#
發(fā)表于 2025-3-30 04:23:45 | 只看該作者
The Easier Waring Problem,roblem is .. So to date, the “easier” Waring problem is not easier than the Waring problem. However, the best bounds for small . are derived in an elementary manner from solutions to the Prouhet-Tarry-Escott problem. This is discussed later in this chapter.
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