Results 11 to 20 of about 84,599 (243)
On the Waring--Goldbach problem for eighth and higher powers [PDF]
, 2015 Recent progress on Vinogradov's mean value theorem has resulted in improved estimates for exponential sums of Weyl type. We apply these new estimates to obtain sharper bounds for the function $H(k)$ in the Waring--Goldbach problem.
Angel V. Kumchev, D. Wooley, Trevor
core +4 more sources
Mordell’s exponential sum estimate revisited [PDF]
Journal of the American Mathematical Society, 2005 The aim of this paper is to extend recent work of S. Konyagin and the author on Gauss sum estimates for large degree to the case of ‘sparse’ polynomials. In this context we do obtain a nearly optimal result, improving on the works of Mordell and of Cochrane and Pinner.
openaire +2 more sources
Exponential sums with reducible polynomials
Discrete Analysis, 2019 Exponential sums with reducible polynomials, Discrete Analysis 2019:15, 31 pp. A sequence $(a_n)$ of real numbers in the interval $[0,1]$ is said to be _equidistributed_ if for every subinterval $[a,b]$ of $[0,1]$, the proportion of the $a_n$ that live
Cécile Dartyge, Greg Martin
doaj +1 more source
On Congruences with Products of Variables from Short Intervals and Applications [PDF]
, 2012 We obtain upper bounds on the number of solutions to congruences of the type $$ (x_1+s)...(x_{\nu}+s)\equiv (y_1+s)...(y_{\nu}+s)\not\equiv0 \pmod p $$ modulo a prime $p$ with variables from some short intervals.
E. Shparlinski +4 more
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Parameter estimation for exponential sums by approximate Prony method [PDF]
Signal Processing, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daniel Potts, Manfred Tasche
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Explicit constructions of RIP matrices and related problems [PDF]
, 2010 We give a new explicit construction of $n\times N$ matrices satisfying the Restricted Isometry Property (RIP). Namely, for some c>0, large N and any n satisfying N^{1-c} < n < N, we construct RIP matrices of order k^{1/2+c}.
Denka Kutzarova +10 more
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The distribution of the maximum of character sums
, 2012 We obtain explicit bounds on the moments of character sums, refining estimates of Montgomery and Vaughan. As an application we obtain results on the distribution of the maximal magnitude of character sums normalized by the square root of the modulus ...
Granville +2 more
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Moments and oscillations of exponential sums related to cusp forms
, 2016 We consider large values of long linear exponential sums involving Fourier coefficients of holomorphic cusp forms. The sums we consider involve rational linear twists $e(nh/k)$ with sufficiently small denominators.
Vesalainen, Esa V.
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Multiple Exponential and Character Sums with Monomials
, 2013 We obtain new bounds of multivariate exponential sums with monomials, when the variables run over rather short intervals. Furthermore, we use the same method to derive estimates on similar sums with multiplicative characters to which previously known ...
Shparlinski, Igor
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Affine extractors over large fields with exponential error
, 2014 We describe a construction of explicit affine extractors over large finite fields with exponentially small error and linear output length. Our construction relies on a deep theorem of Deligne giving tight estimates for exponential sums over smooth ...
Bourgain, Jean +2 more
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