IGUSA’S CONJECTURE FOR EXPONENTIAL SUMS: OPTIMAL ESTIMATES FOR NONRATIONAL SINGULARITIES [PDF]
Forum of Mathematics, Pi, 2019 We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a certain power condition and use it to prove several generalizations of Igusa’s conjecture on exponential sums, with the log canonical threshold in the exponent of ...
RAF CLUCKERS +2 more
doaj +2 more sources
Restriction of Exponential Sums to Hypersurfaces [PDF]
International mathematics research notices, 2021 We prove moment inequalities for exponential sums with respect to singular measures, whose Fourier decay matches those of curved hypersurfaces. Our emphasis will be on proving estimates that are sharp with respect to the scale parameter $N$, apart from
C. Demeter, B. Langowski
semanticscholar +1 more source
A new kth derivative estimate for exponential sums via Vinogradov’s mean value [PDF]
Proceedings of the Steklov Institute of Mathematics, 2017 We give a slight refinement to the process by which estimates for exponential sums are extracted from bounds for Vinogradov’s mean value. Coupling this with the recent works of Wooley, and of Bourgain, Demeter and Guth, providing optimal bounds for the ...
D. R. Heath-Brown
semanticscholar +2 more sources
Sharp Estimates for Proximity of Geometric and Related Sums Distributions to Limit Laws
Mathematics, 2022 The convergence rate in the famous Rényi theorem is studied by means of the Stein method refinement. Namely, it is demonstrated that the new estimate of the convergence rate of the normalized geometric sums to exponential law involving the ideal ...
A. Bulinski, N. Slepov
semanticscholar +1 more source
Multilinear exponential sums with a general class of weights [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2019 In this paper we obtain some new estimates for multilinear exponential sums in prime fields with a more general class of weights than previously considered.
Bryce Kerr, Simon Macourt
semanticscholar +1 more source
Moment estimates for exponential sums over k-free numbers [PDF]
, 2014 We investigate the size of L^p-integrals for exponential sums over k-free numbers and prove essentially tight bounds.
E. Keil
semanticscholar +1 more source
Global Gaussian Estimates for the Heat Kernel of Homogeneous Sums of Squares [PDF]
Potential Analysis, 2020 Let H = ∑ j = 1 m X j 2 − ∂ t ${\mathscr{H}}={\sum }_{j=1}^{m}{X_{j}^{2}}-\partial _{t}$ be a heat-type operator in ℝ n + 1 $\mathbb {R}^{n+1}$ , where X = { X _1,…, X _ m } is a system of smooth Hörmander’s vector fields in ℝ n $\mathbb {R}^{n}$ , and ...
Stefano Biagi, M. Bramanti
semanticscholar +1 more source
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
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
core +1 more source
Dependence of accuracy of ESPRIT estimates on signal eigenvalues: the case of a noisy sum of two real exponentials [PDF]
PAMM, 2008 AbstractThis paper is devoted to estimation of parameters for a noisy sum of two real exponential functions. Singular Spectrum Analysis is used to extract the signal subspace and then the ESPRIT method exploiting signal subspace features is applied to obtain estimates of the desired exponential rates.
Theodore, Alexandrov +2 more
openaire +2 more sources