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On the Number of Real Roots of a Random Algebraic Equation
Author(s) -
Littlewood J. E.,
Offord A. C.
Publication year - 1938
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s1-13.4.288
Subject(s) - citation , algebraic number , mathematics , library science , computer science , mathematical analysis
1 . SOME time ago Littlewood and Offordt gave estimates of the number of real roots that an equation of degree n selected at random might be expected to have for various classes of equations in which the coefficients were selected on some probability basis . They found that, when each coefficient was treated on the same basis, the results were practically the same in all cases considered and agreed with those found for the family of equations fn(x) = 1+ElX+E2x2+. ..+En xn = 0 (1 .1) in which each E,,, v = 1, 2, . . ., n, is + 1 or -1 with equal probability . The object of this paper is to give a refinement of their result . We shall prove THEOREM . The number of real roots of most of the equations