Exponential sums and lattice points III

By M. Huxley. 2003

518 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/0453f2532112340f9fbfc6f41dfc39f4e2dc8798

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In Algebra and Number Theory

In Numerical Analysis

Citations in the corpus

Exponential Sums and the Riemann Zeta Function V (2005, background): “This paper and [7] formed one long preprint, in which xx 4, 5 and 6 were xx 6, 7 and 8; subsequent papers [8] and [9] may refer to Lemma 6.”
On the Gcd-Sum Function (2008, unknown): “The latest result reads ∆(x) ≪ x131/416(log x)26947/8320, (2) due to Huxley [4].”
Measurement of Areas on a Sphere Using Fibonacci and Latitude–Longitude Lattices (2009, methodology): “The number of points of a regular square lattice enclosed by a sufficiently smooth, closed curve placed at random can be expressed as (Huxley 2003) Pin = AM2 + D, (17) where A is the area enclosed by the curve, M is the inverse to the lattice spacing, and D is the discrepancy.”
Lattice points in large regions and related arithmetic functions: Recent developments in a very classic topic (2004, background): “Huxley [43], 2003, improved this result and obtained P (x;CD2) ≪ x 131 208 (log x) 18637 8320 , 131 208 = 0, 6298 .”
Automorphic distributions, L-functions, and Voronoi summation for GL(3) (2004, background): “This formula is actually due to Wilton – see [ 18 ] – and is not among the formulas predicted by Voronoi.”
On higher-power moments of $\Delta(x)$(III) (2008, result): “Similar results are also established for some other well-known error terms in the analytic number theory .”
Multiplicative Arithmetic Functions of Several Variables: A Survey (2013, unknown): “Huxley [32].”
Hyperuniform states of matter (2018, unknown): “[370] and references therein.”
Strichartz estimates for Schrödinger equations on irrational tori (2013, methodology): “While the proof in [11] is based on Jarńık’s argument [27], the proof in [15] is based on Huxley’s counting estimate [24].”
Euler's constant: Euler's work and modern developments (2013, unknown): “Concerning upper bounds, a long sequence of improvements in exponent bounds has arrived at the current record θ ≤ 131416 ≈ 0.31490, obtained by Huxley ([168], [169]) in 2005.”
Summation formulas, from Poisson and Voronoi to the present (2003, background): “A more serious limitation of the argument above is the use of (6.11) to estimate the size of J1. Various authors have done better by taking advantage of the oscillation of J1 [7,8,13,16,17]; the current record bound for �(X) is O(X23/73+ǫ) [ 10 ].”