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Binary sequences and lattices constructed by discrete logarithms
AIMS Mathematics, 2022 In 1997, Mauduit and Sárközy first introduced the measures of pseudorandomness for binary sequences. Since then, many pseudorandom binary sequences have been constructed and studied. In particular, Gyarmati presented a large family of pseudorandom binary
Yuchan Qi, Huaning Liu
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One kind hybrid character sums and their upper bound estimates [PDF]
Journal of Inequalities and Applications, 2018 The main purpose of this paper is applying the analysis method, the properties of Lucas polynomials and Gauss sums to study the estimation problems of some kind hybrid character sums. In the end, we obtain several sharp upper bound estimates for them. As some applications, we prove some new and interesting combinatorial identities.
Jianhong Zhao, Xiao Wang
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P\'olya-Vinogradov and the least quadratic nonresidue [PDF]
, 2015 It is well-known that cancellation in short character sums (e.g. Burgess' estimates) yields bounds on the least quadratic nonresidue. Scant progress has been made on short character sums since Burgess' work, so it is desirable to find a new approach to ...
Bober, Jonathan, Goldmakher, Leo
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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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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
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Generalised divisor sums of binary forms over number fields [PDF]
, 2016 Estimating averages of Dirichlet convolutions $1 \ast \chi$, for some real Dirichlet character $\chi$ of fixed modulus, over the sparse set of values of binary forms defined over $\mathbb{Z}$ has been the focus of extensive investigations in recent years,
Frei, Christopher, Sofos, Efthymios
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Sub-Weyl subconvexity for Dirichlet L-functions to prime power moduli [PDF]
, 2014 We prove a subconvexity bound for the central value L(1/2, chi) of a Dirichlet L-function of a character chi to a prime power modulus q=p^n of the form L(1/2, chi)\ll p^r * q^(theta+epsilon) with a fixed r and theta\approx 0.1645 < 1/6, breaking the long-
Milićević, Djordje
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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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From Oscillatory Integrals and Sublevel Sets to Polynomial Congruences and Character Sums [PDF]
, 2010 We present a slight extension of a classical lemma of Hensel and give various applications to polynomial congruences and character sums; in particular, we give a new proof of a classical result of Hua on complete exponential sums.
Wright, James
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Character sums to smooth moduli are small
, 2007 Recently, Granville and Soundararajan have made fundamental breakthroughs in the study of character sums. Building on their work and using estimates on short character sums developed by Graham-Ringrose and Iwaniec, we improve the Polya-Vinogradov ...
Davenport +12 more
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