On the Expected Number of Real Zeros of Random Polynomials I. Coefficients with Zero Means

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Previous article Next article On the Expected Number of Real Zeros of Random Polynomials I. Coefficients with Zero MeansI. A. Ibragimov and N. B. MaslovaI. A. Ibragimov and N. B. Maslovahttps://doi.org/10.1137/1116023PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. E. Littlewood and , A. C. Offord, On the number of real roots of a random algebraic equation. I, J. London Math. Soc., 13 (1939), 288–295 0020.13604 CrossrefGoogle Scholar[2] J. E. Littlewood and , A. C. Offord, On the number of real roots of a random algebraic equation. II, Proc. Cambr. Phil. Soc., 35 (1939), 133–148 0021.03702 CrossrefGoogle Scholar[3] J. E. Littlewood and , A. C. Offord, On the number of real roots of a random algebraic equation. III, Rec. Math. [Mat. Sbornik] N.S., 12(54) (1943), 277–286 MR0009656 0061.01801 Google Scholar[4] M. Kac, On the average number of real roots of a random algebraic equation, Bull. Amer. Math. 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Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1963xvi+685 MR0203748 0108.14202 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Random trigonometric polynomials: Universality and non-universality of the variance for the number of real rootsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 58, No. 3 | 1 Aug 2022 Cross Ref Real roots of random polynomials with coefficients of polynomial growth: a comparison principle and applicationsElectronic Journal of Probability, Vol. 26, No. none | 1 Jan 2021 Cross Ref Real zeros of random trigonometric polynomials with pairwise equal blocks of coefficientsRocky Mountain Journal of Mathematics, Vol. 50, No. 4 | 1 Aug 2020 Cross Ref New asymptotics for the mean number of zeros of random trigonometric polynomials with strongly dependent Gaussian coefficientsElectronic Communications in Probability, Vol. 25, No. none | 1 Jan 2020 Cross Ref Non universality for the variance of the number of real roots of random trigonometric polynomialsProbability Theory and Related Fields, Vol. 174, No. 3-4 | 21 September 2018 Cross Ref On Real Zeros of Self-Similar Random Gaussian Polynomials with Decreasing Variances: Apparition of a Phase TransitionBulletin of the Iranian Mathematical Society, Vol. 45, No. 1 | 11 July 2018 Cross Ref Roots of random polynomials with coefficients of polynomial growthThe Annals of Probability, Vol. 46, No. 5 | 1 Sep 2018 Cross Ref Variance of the number of zeroes of shift-invariant Gaussian analytic functionsIsrael Journal of Mathematics, Vol. 227, No. 2 | 21 July 2018 Cross Ref Expected Number of Real Zeros of Gaussian Self-Reciprocal Random Algebraic PolynomialsIranian Journal of Science and Technology, Transactions A: Science, Vol. 42, No. 1 | 3 February 2018 Cross Ref A new test of multivariate nonlinear causalityPLOS ONE, Vol. 13, No. 1 | 5 January 2018 Cross Ref Expected number of real zeros for random orthogonal polynomialsMathematical Proceedings of the Cambridge Philosophical Society, Vol. 164, No. 1 | 27 September 2016 Cross Ref On the number of real roots of random polynomialsCommunications in Contemporary Mathematics, Vol. 18, No. 04 | 1 Aug 2016 Cross Ref CLT for the zeros of classical random trigonometric polynomialsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 52, No. 2 | 1 May 2016 Cross Ref Real roots of random polynomials: expectation and repulsionProceedings of the London Mathematical Society, Vol. 111, No. 6 | 23 November 2015 Cross Ref Expected number of real zeros for random Freud orthogonal polynomialsJournal of Mathematical Analysis and Applications, Vol. 429, No. 2 | 1 Sep 2015 Cross Ref Local Universality of Zeroes of Random PolynomialsInternational Mathematics Research Notices, Vol. 2015, No. 13 | 6 June 2014 Cross Ref Asymptotics of the variance of the number of real roots of random trigonometric polynomialsScience China Mathematics, Vol. 55, No. 11 | 10 November 2012 Cross Ref Around the circular lawProbability Surveys, Vol. 9, No. none | 1 Jan 2012 Cross Ref New features on real zeros of random polynomialsNonlinear Analysis: Theory, Methods & Applications, Vol. 71, No. 12 | 1 Dec 2009 Cross Ref Algebraic polynomials with random non-symmetric coefficientsStatistics & Probability Letters, Vol. 78, No. 11 | 1 Aug 2008 Cross Ref Expected Number of Slope Crossings of Certain Gaussian Random PolynomialsStochastic Analysis and Applications, Vol. 26, No. 2 | 7 Mar 2008 Cross Ref An Example of a Random Polynomial with Unusual Zeros BehaviorTheory of Probability & Its Applications, Vol. 50, No. 3 | 15 August 2006AbstractPDF (138 KB)The expected number of zeros of a random system of $p$-adic polynomialsElectronic Communications in Probability, Vol. 11, No. none | 1 Jan 2006 Cross Ref On the average number of level crossings of certain Gaussian random polynomialsNonlinear Analysis: Theory, Methods & Applications, Vol. 63, No. 5-7 | 1 Nov 2005 Cross Ref Real roots of random polynomials: universality close to accumulation pointsJournal of Physics A: Mathematical and General, Vol. 37, No. 4 | 9 January 2004 Cross Ref On the Expected Number of Real Zeros of Certain Gaussian Random PolynomialsStochastic Analysis and Applications, Vol. 21, No. 1 | 3 Jan 2003 Cross Ref On the Expected Number of Level Crossings of a Random PolynomialJournal of Mathematical Analysis and Applications, Vol. 208, No. 1 | 1 Apr 1997 Cross Ref Random polynomials with complex coefficientsStatistics & Probability Letters, Vol. 27, No. 4 | 1 May 1996 Cross Ref Sharp crossings of a non-stationary stochastic process and its application to random polynomialsStochastic Analysis and Applications, Vol. 14, No. 1 | 3 April 2007 Cross Ref On the number of real roots of a random algebraic equationJournal of the Australian Mathematical Society. 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