scholarly journals Lattice point problems involving index and joint visibility

2019 ◽  
Vol 147 (8) ◽  
pp. 3273-3288 ◽  
Author(s):  
Sneha Chaubey ◽  
Albert Tamazyan ◽  
Alexandru Zaharescu
Keyword(s):  
Lattice Point ◽  
Lattice Point Problems

Some Applications of Fourier series in the Analytic Theory of Numbers

1928 ◽  
Vol 24 (4) ◽  
pp. 585-596 ◽  
Author(s):  
L. J. Mordell
Keyword(s):  
Fourier Series ◽  
Class Number ◽  
Lattice Point ◽  
Zeta Functions ◽  
Gauss Sums ◽  
Analytic Theory ◽  
Quadratic Fields ◽  
Lattice Point Problems ◽  
Theory Of Numbers

It is a familiar fact that an important part is played in the Analytic Theory of Numbers by Fourier series. There are, for example, applications to Gauss' sums, to the zeta functions, to lattice point problems, and to formulae for the class number of quadratic fields.

Two classical lattice point problems

1961 ◽  
Vol 57 (4) ◽  
pp. 699-721 ◽  
Author(s):  
K. S. Gangadharan ◽  
A. E. Ingham
Keyword(s):  
Lattice Point ◽  
Error Term ◽  
Divisor Problem ◽  
Lattice Points ◽  
Classical Lattice ◽  
Rectangular Hyperbola ◽  
Number Of Divisors ◽  
Image Position ◽  
Euler's Constant ◽  
Lattice Point Problems

Let r(n) be the number of representations of n as a sum of two squares, d(n) the number of divisors of n, andwhere γ is Euler's constant. Then P(x) is the error term in the problem of the lattice points of the circle, and Δ(x) the error term in Dirichlet's divisor problem, or the problem of the lattice points of the rectangular hyperbola.

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