Mean square value of exponential sums related to representation of integers as sum of two squares

• Autorzy: Pavel M. Bleher , Freeman J. Dyson
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1994
• Tom: 68
• Numer: 1
• Strony: 71-84

Daty

wydano

1994

otrzymano

1993-11-03

poprawiono

1994-02-01

Twórcy

autor

Pavel M. Bleher

• School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A.

autor

Freeman J. Dyson

• School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A.

Bibliografia

• [B] P. M. Bleher, On the distribution of the number of lattice points inside a family of convex ovals, Duke Math. J. 67 (1992), 461-481.
• i[BCDL] P. M. Bleher, Z. Cheng, F. J. Dyson and J. L. Lebowitz, Distribution of the error term for the number of lattice points inside a shifted circle, Comm. Math. Phys. 154 (1993), 433-469.
• [BD] P. M. Bleher and F. J. Dyson, The variance of the error function in the shifted circle problem is a wild function of the shift, Comm. Math. Phys., to appear.
• [C] H. Cramér, Über zwei Sätze von Herrn G. H. Hardy, Math. Z. 15 (1922), 201-210.
• [H] G. H. Hardy, The average order of the arithmetic functions P(x) and Δ(x), Proc. London Math. Soc. 15 (1916), 192-213.
• [HL] G. H. Hardy and J. E. Littlewood, Tauberian theorems concerning power series and Dirichlet series whose coefficients are positive, Proc. London Math. Soc. 13 (1914), 174.
• [HW] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th ed., Oxford, 1960.
• [H-B] D. R. Heath-Brown, The distribution and moments of the error term in the Dirichlet divisor problem, Acta Arith. 60 (1992), 389-415.