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Abstrakty
For positive integers m and N, we estimate the rational exponential sums with denominator m over the reductions modulo m of elements of the set F(N) = {s/r : r, s ∈ Z, gcd(r, s) = 1, N ≥ r > s ≥ 1} of Farey fractions of order N (only fractions s/r with gcd(r, m) = 1 are considered).
Słowa kluczowe
Wydawca
Rocznik
Tom
Strony
101--107
Opis fizyczny
Bibliogr. 13 poz.
Twórcy
autor
- Department of Computing, Macquarie University, Sydney, NSW 2109, Australia, igor@ics.mq.edu.au
Bibliografia
- [1] E. Alkan, A. H. Ledoan, M. Vajaitu and A. Zaharescu, Discrepancy of fractions with divisibility constraints, Monatsh. Math. 149 (2006), 179-192.
- [2] E. Alkan, M. Xiong and A. Zaharescu, Quotients of values of the Dedekind eta function, Math. Ann. 342 (2008), 157-176.
- [3] R. Balasubramanian, S. Kanemitsu and M. Yoshimoto, Euler products, Farey series, and the Riemann hypothesis, Publ. Math. Debrecen 69 (2006), 1-16.
- [4] C. Cobeli and A. Zaharescu, The Haros-Farey sequence at two hundred years, Proc. Acta Univ. Apulensis Math. Inform. 5 (2003), 1-38.
- [5] A. C. Cojocaru and I. E. Shparlinski, Distribution of Farey fractions in residue classes and Lang-Trotter conjectures on average, Proc. Amer. Math. Soc. 136 (2008), 1977-1986.
- [6] M. Drmota and R. Tichy, Sequences, Discrepancies and Applications, Springer, Berlin, 1997.
- [7] A. Fujii, On the Farey series and the Riemann hypothesis, Comment. Math. Univ. St. Pauli 54 (2005), 211-235.
- [8] A. Fujii, On the Farey series and the Hecke L-functions, Comment. Math. Univ. St. Pauli 56 (2007), 97-162.
- [9] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford Univ. Press, Oxford, 1979.
- [10] H. Iwaniec and E. Kowalski, Analytic Number Theory, Amer. Math. Soc., Providence, RI, 2004.
- [11] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley-Interscience Publ., 1974.
- [12] I. E. Shparlinski, Primitive points on a modular hyperbola, Bull. Polish Acad. Sci. Math. 54 (2006), 193-200.
- [13] I. E. Shparlinski, Distribution of inverses and multiples of small integers and the Sato-Tate conjecture on average, Michigan Math. J. 56 (2008), 99-111.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-BAT5-0040-0013