On Numbers with a Large Prime Factor II

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Authors

  • Matti Jutila
     University of Turku, Department of Mathematics, Turku ,FI

Abstract

For positive integers u, k let P(u, k) stand for the largest prime factor of the number (u + 1).. .(u + k). For x > 0, z > 0 , A(z, x) = (log z/log x)2, for real x, e(x) - e2Ï€ix, [x] = the largest integer not exceeding x, {x} = x - [x]. c1, c2, . . . are positive constants. The constants implied by the symbols <, >, and 0( ) are absolute unless otherwise indicated.

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Published

1974-12-01

How to Cite

Jutila, M. (1974). On Numbers with a Large Prime Factor II. The Journal of the Indian Mathematical Society, 38(1-4), 125–130. Retrieved from http://informaticsjournals.com/index.php/jims/article/view/16686

Issue

Volume 38, Issue 1-4, March-December 1974

Section

Articles

License

Copyright (c) 1974 Matti Jutila

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

 

References

M. JUTILA: On numbers with a large prime factor. Jour. Ind. Math. Soc. 37(1973)43-53.

A.A. KARAZUBA: Estimates for trigonometrical sums by the method of I.M.Vinogradov and their applications (Russian), Trudy Mat. Inst. Stekloff 112:1(1971), 241-255.

-5. K. RAMACHANDRA: A note on numbers with a large prime factor I, J. Loudon Math. Soc. 2(1969), 303-306: 11,J. Indian Math. Soc. 34 (1970), 39-48; III, Acta Arith. 19 (1971), 49-62.

E.C. TITCHMARSH: The Theory of the Riemann Zeta-function, Oxford University Press (1951).

I.M. VINOGRADOV: The method of trigonometrical sums in the theory of numbers (Russian). Izd."Nauka", Moscow(1971).

A. WALFISZ: Weylsche Exponentialsummen in der neueren Zahlentheorie. VEB Deutscher Verlag der Wissenschaften, Berlin (1963).