Primitive lattice points in convex planar domains

• Autorzy: Martin N. Huxley , Werner Georg Nowak
• Języki publikacji: EN

Słowa kluczowe

EN

primitive lattice points; Riemann Hypothesis

Kategorie tematyczne

• 11M41: Other Dirichlet series and zeta functions
• 11P21: Lattice points in specified regions
• 11M26: Nonreal zeros of ζ ( s ) and L ( s , χ ) ; Riemann and other hypotheses

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1996
• Tom: 76
• Numer: 3
• Strony: 271-283

Daty

wydano

1996

otrzymano

1995-07-10

poprawiono

1995-12-19

Twórcy

autor

Martin N. Huxley

• School of Mathematics, University of Wales, 23 Senghenydd Road, Cardiff CF2 4YH, Wales, Great Britain

autor

Werner Georg Nowak

• Institut für Mathematik, Universität für Bodenkultur, A-1180 Wien, Austria

Bibliografia

• [1] T. M. Apostol, Introduction to Analytic Number Theory, Springer, New York, 1976.
• [2] R. C. Baker, The square-free divisor problem, Quart. J. Math. Oxford 45 (1994), 269-277.
• [3] J. L. Hafner, New omega theorems for two classical lattice point problems, Invent. Math. 63 (1981), 181-186.
• [4] D. R. Heath-Brown, The Piatetski-Shapiro prime-number theorem, J. Number Theory 16 (1983), 242-266.
• [5] D. Hensley, The number of lattice points within a contour and visible from the origin, Pacific J. Math. 166 (1994), 295-304.
• [6] E. Hlawka, Über Integrale auf konvexen Körpern I, Monatsh. Math. 54 (1950), 1-36.
• [7] E. Hlawka, Über Integrale auf konvexen Körpern II, Monatsh. Math. 54 (1950), 81-99.
• [8] E. Hlawka, Über die Zetafunktion konvexer Körper, Monatsh. Math. 54 (1950), 100-107.
• [9] M. N. Huxley, Exponential sums and lattice points II, Proc. London Math. Soc. 66 (1993), 279-301.
• [10] M. N. Huxley, The mean lattice point discrepancy, Proc. Edinburgh Math. Soc. 38 (1995), 523-531.
• [11] M. N. Huxley, Area, Lattice Points, and Exponential Sums, Oxford University Press, to appear.
• [12] A. Ivić, The Riemann Zeta-function, Wiley, New York, 1985.
• [13] I. Kátai, The number of lattice points in a circle, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 8 (1965), 39-60.
• [14] E. Krätzel, Lattice Points, Deutsch. Verlag Wiss., Berlin, 1988.
• [15] H. L. Montgomery and R. C. Vaughan, The distribution of squarefree numbers, in: Recent Progress in Analytic Number Theory, Proc. Durham Sympos. 1979, Vol. I, H. Halberstam and C. Hooley (eds.), Academic Press, London, 1981, 247-256.
• [16] B. Z. Moroz, On the number of primitive lattice points in plane domains, Monatsh. Math. 99 (1985), 37-43.
• [17] W. G. Nowak, An Ω-estimate for the lattice rest of a convex planar domain, Proc. Roy. Soc. Edinburgh Sect. A 100 (1985), 295-299.
• [18] W. G. Nowak, On the average order of the lattice rest of a convex planar domain, Proc. Cambridge Philos. Soc. 98 (1985), 1-4.
• [19] W. G. Nowak, Primitive lattice points in rational ellipses and related arithmetic functions, Monatsh. Math. 106 (1988), 57-63.
• [20] W. G. Nowak and M. Schmeier, Conditional asymptotic formulae for a class of arithmetic functions, Proc. Amer. Math. Soc. 103 (1988), 713-717.
• [21] K. Prachar, Primzahlverteilung, Springer, Berlin, 1957.