Titlebook: Number Theory – Diophantine Problems, Uniform Distribution and Applications; Festschrift in Honou Christian Elsholtz,Peter Grabner Book 201

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同音

A Discrepancy Problem: Balancing Infinite Dimensional Vectors,ously for all integers . ≥ 1, every (finite) arithmetic progression of difference . has discrepancy ..(.) ≤ .., independently of the starting point and the length of the arithmetic progression. Formally, for every . > 0 there exists a function . such that . for all sufficiently large . ≥ ..(.). This

開(kāi)始發(fā)作

Squares with Three Nonzero Digits,uations of the shape . where . is an odd prime, . > . > 0 and ..,?| . |,?. < ., either arise from “obvious” polynomial families or satisfy . ≤ 3. Our arguments rely upon Padé approximants to the binomial function, considered .-adically.

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內(nèi)行

Diversity in Parametric Families of Number Fields, Dvornicich and Zannier implies that, for large ., among the number fields . there are at least .∕ log. distinct; here, . > 0 depends only on the degree . and the genus . = .(.). We prove that there are at least .∕(log.). distinct fields, where . > 0 depends only on . and ..

PALSY

,On the Discrepancy of Halton–Kronecker Sequences,t for . algebraic we have . for all . > 0. On the other hand, we show that for . with bounded continued fraction coefficients we have . which is (almost) optimal since there exist . with bounded continued fraction coefficients such that ..

Anguish

More on Diophantine Sextuples,rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely many rational Diophantine quintuples. In 1999, Gibbs found the first example of a rational Diophantine sextuple, and Dujella, Kazalicki, Miki? and Szikszai recently proved that there exist infinitely

parallelism

Spinal-Fusion