A Remark on Cavitational Flow.

نویسندگان

  • P R Garabedian
  • H L Royden
چکیده

pp. 76-83. Cf. also R. Brauer, Bull. Am. Math. Soc., 51, 749-755 (1945). For calling our attention to the first reference, we are indebted to Dr. Ernst Snapper; for the third, to Dr. H. N. Shapiro. 4 Cipolla, Periodico. di Mat., 22, 36-41 (1907). For every m in (5a) equal to zero then N reduces to the number of sets of roots of (A), a fortnula known to V. A. Lebesgue, for n = 1, and this was employed to advantage by S. Schwarz, Quart. J. Math., 19, 160-163 (1948), in order to obtain a theorem concerning the existence of solutions of (6). Cipolla gave (5a) only for n = 1, k = 1, s = 1, but the extension is immediate. I This Corollary together with the formula (7) give a number of solutions of (6) in a finite field F(pP) with the coefficients in F(pf) and cl, c2, . . . , cs 0 both for the case where we include zero values for the x's and when we do not. These formulas are all in terms of the 4, numbers defined in (8). For previous references concerning the application of the number (for general n, cf. Stickelberger; Davenport-Hasse, loc. cit.)

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عنوان ژورنال:
  • Proceedings of the National Academy of Sciences of the United States of America

دوره 38 1  شماره 

صفحات  -

تاریخ انتشار 1952