Abstract
We estimate the number of relatively r-prime lattice points in
References
[1] S. J. Benkoski, The probability that k positive integers are relatively r-prime, J. Number Theory 8 (1976), no. 2, 218–223. 10.1016/0022-314X(76)90103-7Suche in Google Scholar
[2] J. Bourgain, Decoupling, exponential sums and the Riemann zeta function, J. Amer. Math. Soc. 30 (2017), no. 1, 205–224. 10.1090/jams/860Suche in Google Scholar
[3] M. N. Huxley and N. Watt, Hybrid bounds for Dirichlet’s L-function, Math. Proc. Cambridge Philos. Soc. 129 (2000), no. 3, 385–415. 10.1017/S0305004100004527Suche in Google Scholar
[4] H. Iwaniec and E. Kowalski, Analytic Number Theory, Amer. Math. Soc. Colloq. Publ. 53, American Mathematical Society, Providence, 2004. 10.1090/coll/053Suche in Google Scholar
[5] S. Lang, Algebraic Number Theory, 2nd ed., Grad. Texts in Math. 110, Springer, New York, 1994. 10.1007/978-1-4612-0853-2Suche in Google Scholar
[6] D. N. Lehmer, Asymptotic evaluation of certain totient sums, Amer. J. Math. 22 (1900), no. 4, 293–335. 10.2307/2369728Suche in Google Scholar
[7] B. D. Sittinger, The probability that random algebraic integers are relatively r-prime, J. Number Theory 130 (2010), no. 1, 164–171. 10.1016/j.jnt.2009.06.008Suche in Google Scholar
[8] W. Takeda, The distribution of lattice points with relatively r-prime, preprint (2017), https://arxiv.org/abs/1704.02115, to appear in Algebra Discrete Math. Suche in Google Scholar
[9] W. Takeda, Visible lattice points and the extended Lindelöf hypothesis, J. Number Theory 180 (2017), 297–309. 10.1016/j.jnt.2017.04.002Suche in Google Scholar
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- A generalized uniqueness theorem and the graded ideal structure of Steinberg algebras
- Positive solutions for nonlinear nonhomogeneous parametric Robin problems
- Period relations for cusp forms of GSp4
- A generalization of a graph theory Mertens’ theorem: Galois covering case
- Commutators of the fractional integrals for second-order elliptic operators on Morrey spaces
- Vojta’s conjecture on rational surfaces and the abc conjecture
- The least unramified prime which does not split completely
- The ω-inequality problem for concatenation hierarchies of star-free languages
- Higher weight on GL(3). I: The Eisenstein series
- Fourier transforms of powers of well-behaved 2D real analytic functions
- Parabolic conformally symplectic structures I; definition and distinguished connections
- The quasi-arithmetic means and Cartan barycenters of compactly supported measures
- Estimates of lattice points in the discriminant aspect over abelian extension fields
- On Hecke eigenvalues of Siegel modular forms in the Maass space
- Harmonicity and minimality of complex and quaternionic radial foliations
Artikel in diesem Heft
- Frontmatter
- A generalized uniqueness theorem and the graded ideal structure of Steinberg algebras
- Positive solutions for nonlinear nonhomogeneous parametric Robin problems
- Period relations for cusp forms of GSp4
- A generalization of a graph theory Mertens’ theorem: Galois covering case
- Commutators of the fractional integrals for second-order elliptic operators on Morrey spaces
- Vojta’s conjecture on rational surfaces and the abc conjecture
- The least unramified prime which does not split completely
- The ω-inequality problem for concatenation hierarchies of star-free languages
- Higher weight on GL(3). I: The Eisenstein series
- Fourier transforms of powers of well-behaved 2D real analytic functions
- Parabolic conformally symplectic structures I; definition and distinguished connections
- The quasi-arithmetic means and Cartan barycenters of compactly supported measures
- Estimates of lattice points in the discriminant aspect over abelian extension fields
- On Hecke eigenvalues of Siegel modular forms in the Maass space
- Harmonicity and minimality of complex and quaternionic radial foliations