Transcranial Magnetic Stimulation over the Left Inferior Parietal Lobule Facilitates Early-Stage Processing During Natural Chinese-English Bilingual Reading. [PDF]
Brain SciWu J +5 more
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Implications of Yedoma bank outcrop on the Arctic river sediment transport. [PDF]
Sci RepChalov S +9 more
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Social avoidance can be quantified as navigation in abstract social space. [PDF]
Commun PsycholSchafer M, Schiller D.
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Polygenic risk moderation of stressful life events in alcohol use disorder severity. [PDF]
BMC PsychiatryAgabani Z +4 more
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Additive impulsivity and emotion dysregulation in adolescents with comorbid bipolar and substance use disorder: a cross-sectional factorial study. [PDF]
Front PsychiatryOcakoglu FT +5 more
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Estimates of character sums in finite fields
Mathematical Notes, 2010 Suppose \(p\) is a prime and \(\{\omega_1,\dots,\omega_n\}\) is a basis of \(\mathbb F_{p^n}\) over \(\mathbb F_p\). Suppose \(B\) is an \(n\)-dimensional parallelepiped with edges \(H_1,\dots,H_n\), that is \[ B=\left\{\sum_{x=1}^n x_i\omega_i:N_i+1\leq x_i\leq N_i+H_i, i=1,\dots,n\right\}, \] where \(0\leq N_i0\), there is a natural number \(k ...
S V Konyagin, Konyagin S V
exaly +3 more sources
Some Estimates for Character Sums and Applications
Designs, Codes and Cryptography, 2001 Let \(p\) be a prime number, \(F_{q}\) a finite field with \(q=p^{ \nu}\) elements, \(S\) a subset of \(F_{q}\), and \( \chi\) a nontrivial multiplicative character of the field \(F_{q}\) of order \(s \geq 2\). If \(n \geq 2\) is an arbitrary integer satisfying \(n \not\equiv 0\pmod s\), the author proves that there exists a monic irreducible ...
Arne Winterhof
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Lower estimates of sums of polynomial characters
Mathematical Notes of the Academy of Sciences of the USSR, 1973 An infinite sequence of primes p is formulated, and for each p polynomials of formaxn+b, (a, p)=(b, p)=1, are indicated such that $$\sum\nolimits_{x = 1}^p {\left( {\frac{{ax^n + b}}{p}} \right) = p,n \asymp \frac{p}{{log p}}.}$$
Anatolij A. Karatsuba
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The Character Sum Estimate with r = 3
Journal of the London Mathematical Society, 1986 This paper is the culmination of the author's recent efforts to extend his well-known character sum estimates to arbitrary moduli. He shows that for any non-principal character \(\chi\) modulo \(k\) and arbitrary positive integers \(N\) and \(H\) the estimate \[ \sum^{N+H}_{n=N+1}\chi (n) \ll_{\varepsilon} H^{1-(1/r)} k^{(r+1)/4r^ 2+\varepsilon}\tag{*}
D. A. Burgess
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