The distribution and moments of the error term in the Dirichlet divisor problem

• Autorzy: D. R. Heath-Brown
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1991-1992
• Tom: 60
• Numer: 4
• Strony: 389-415

Daty

wydano

1992

otrzymano

1991-02-20

poprawiono

1991-05-07

Twórcy

autor

D. R. Heath-Brown

• Magdalen College, Oxford OX1 4AU, England

Bibliografia

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• [2] F. V. Atkinson, The mean-value of the Riemann zeta function, Acta Math. 81 (1949), 353-376.
• [3] H. Cramér, Über zwei Sätze von Herrn G. H. Hardy, Math. Z. 15 (1922), 201-210.
• [4] D. R. Heath-Brown, The mean value theorem for the Riemann zeta-function, Mathematika 25 (1978), 177-184.
• [5] D. R. Heath-Brown and M. N. Huxley, Exponential sums with a difference, Proc. London Math. Soc. (3) 61 (1990), 227-250.
• [6] A. Ivić, The Riemann Zeta-function, Wiley, New York 1985.
• [7] H. Iwaniec and C. J. Mozzochi, On the divisor and circle problems, J. Number Theory 29 (1988), 60-93.
• [8] K.-L. Kueh, The moments of infinite series, J. Reine Angew. Math. 385 (1988), 1-9.
• [9] E. C. Titchmarsh, The Theory of the Riemann Zeta-function, 2nd ed., Oxford Univ. Press, Oxford 1986.
• [10] K.-C. Tong, On divisor problems, III, Acta Math. Sinica 6 (1956), 515-541.
• [11] K.-M. Tsang, Higher power moments of Δ(x), E(t) and P(x), Proc. London Math. Soc. (3), to appear.
• [12] G. Voronoï, Sur une fonction transcendante et ses applications à la sommation de quelques séries, Ann. Sci. École Norm. Sup. (3) 21 (1904), 207-267 & 459-533.