Zobrazeno 1 - 10 of 464 pro vyhledávání: '"J. Bourgain"'
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On the correlation of the Moebius functionwith rank-one systems
Autor: J. Bourgain
Publikováno v: Journal d'Analyse Mathématique. 120:105-130
We explore the “Moebius disjointness property” in the special context of rank-one transformations and verify this phenomenon for many of the “classical” models.
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::c33ea9370eb4ae26cba2c625e34daaa1
https://doi.org/10.1007/s11854-013-0016-z
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Möbius-Walsh correlation bounds and an estimate of Mauduit and Rivat
Autor: J. Bourgain
Publikováno v: Journal d'Analyse Mathématique. 119:147-163
We establish small correlation bounds for the Mobius function and the Walsh system, answering affirmatively a question posed by G. Kalai [Ka]. The argument is based on generalizing the approach of Mauduit and Rivat [M-R] in order to treat Walsh funct
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::792a2c59625bda67d42cbd8baeed1507
https://doi.org/10.1007/s11854-013-0005-2
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4
Exponential sum estimates over a subgroup in an arbitrary finite field
Autor: A. Glibichuk, J. Bourgain
Publikováno v: Journal d'Analyse Mathématique. 115:51-70
Let F q be the finite field consisting of q = p r elements and yy an additive character of the field F q . Take an arbitrary multiplicative subgroup H of size |H| > q C/(log log q) for some constant C > 0 not largely contained in any multiplicative s
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::86938e9fdcd3495cfda4f63dea686daa
https://doi.org/10.1007/s11854-011-0023-x
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5
On the distribution of the residues of small multiplicative subgroups of $$ \mathbb{F}_p $$
Autor: J. Bourgain
Publikováno v: Israel Journal of Mathematics. 172:61-74
Distributional properties of small multiplicative subgroups of \( \mathbb{F}_p \) are obtained. In particular, it is shown that if H < \( \mathbb{F}_p^* \) is of size larger than polylogarithmic in p, then, letting β < 1 be a fixed exponent, most el
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::c1c8eedb0502824d2b4919066ce24bb6
https://doi.org/10.1007/s11856-009-0063-4
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Exponential sum estimates over subgroups and almost subgroups of $$ \mathbb{Z}_{Q}^{*} $$ , where Q is composite with few prime factors
Autor: J. Bourgain, Mei-Chu Chang
Publikováno v: GAFA Geometric And Functional Analysis. 16:327-366
In this paper we extend the exponential sum results from [BK] and [BGK] for prime moduli to composite moduli q involving a bounded number of prime factors. In particular, we obtain nontrivial bounds on the exponential sums associated to multiplicativ
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::97d6bd4e474ee7de6ecf67c7ba887a31
https://doi.org/10.1007/s00039-006-0558-7
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9
MORE ON THE SUM-PRODUCT PHENOMENON IN PRIME FIELDS AND ITS APPLICATIONS
Autor: J. Bourgain
Publikováno v: International Journal of Number Theory. :1-32
In this paper we establish new estimates on sum-product sets and certain exponential sums in finite fields of prime order. Our first result is an extension of the sum-product theorem from [8] when sets of different sizes are involed. It is shown that
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::0ca917ed7692a7f0524f5c11181e374f
https://doi.org/10.1142/s1793042105000108
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10
Recent progress on quasi-periodic lattice Schrödinger operators and Hamiltonian PDEs
Autor: J Bourgain
Publikováno v: Russian Mathematical Surveys. 59:231-246
This is a survey of recent investigations of quasi-periodic localization on lattices (of both methods based on perturbation theory and non-perturbative methods) and of applications of KAM theories in connection with infinite-dimensional Hamiltonian s
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::eb6b4e32384b7b37a1ae76dba46daf39
https://doi.org/10.1070/rm2004v059n02abeh000716
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