Results 1 to 10 of about 9,690 (225)
EXPONENTIAL SUMS OVER PRIMES IN SHORT INTERVALS AND AN APPLICATION TO THE WARING–GOLDBACH PROBLEM [PDF]
Mathematika, 2016 Let $ (n)$ be the von Mangoldt function, $x$ real and $2\leq y \leq x$. This paper improves the estimate on the exponential sum over primes in short intervals \[ S_k(x,y; ) = \sum_{x< n \leq x+y} (n) e\left( n^k \right) \] when $k\geq 3$ for $ $ in the minor arcs.
Bingrong Huang
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On exponential sums involving Fourier coefficients of cusp forms over primes
Journal of Number Theory, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The twin prime conjecture [PDF]
, 2014 This is an exposition of recent developments in the theory of bounded differences between primes. Readers are expected to be beginners of analytic number theory.
Motohashi, Yoichi
core
Comptes Rendus. Mathématique, 2003 Our first result is a ‘sum–product’ theorem for subsets A of the finite field 𝔽 p , p prime, providing a lower bound on max(|A+A|,|A·A|). As corollary, the second and main result provides new bounds on exponential sums associated to subgroups of the multiplicative group 𝔽 p * .
Bourgain, Jean, Konyagin, S. V.
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Exponential sums over primes are unbounded
We prove prime exponential sums have no better than square root cancellation on average on short intervals, in the sense that $$\frac{1}{x} \sum_{-y< n\le x} \left|\sum_{\substack{n< m \le n+y\\ 1\le m \le x}} Λ(m) \mathrm{e}(αm)\right|^2 \gg y\log y$$ whenever $y \ll x^{1/3-\varepsilon}.$ This answers a question of Ramaré by proving the lower ...
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On sums of coefficients of polynomials related to the Borwein conjectures. [PDF]
Ramanujan J, 2022 Goswami A, Pantangi VRT.
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Value distribution for eigenfunctions of desymmetrized quantum maps
, 2001 We study the value distribution and extreme values of eigenfunctions for the ``quantized cat map''. This is the quantization of a hyperbolic linear map of the torus. In a previous paper it was observed that there are quantum symmetries of the quantum map
Kurlberg, Par, Rudnick, Zeev
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Bounds for the Diameters of Orbital Graphs of Affine Groups. [PDF]
Vietnam J Math, 2023 Maróti A, Skresanov SV.
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Along the Lines of Nonadditive Entropies: q-Prime Numbers and q-Zeta Functions. [PDF]
Entropy (Basel), 2021 Borges EP, Kodama T, Tsallis C.
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About the complexity of two-stage stochastic IPs. [PDF]
Math Program, 2022 Klein KM.
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