Lattice Point Problems: Crossroads of Number Theory, Probability Theory and Fourier Analysis

2004 ◽  
pp. 1-35 ◽  
Author(s):  
József Beck
Keyword(s):  
Probability Theory ◽  
Number Theory ◽  
Fourier Analysis ◽  
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.

scholarly journals Some Results in the Fourier Analysis

1966 ◽  
Vol 27 (1) ◽  
pp. 55-59
Author(s):  
Tikao Tatuzawa
Keyword(s):  
Number Theory ◽  
Euclidean Space ◽  
Fourier Analysis ◽  
Analytic Number Theory ◽  
Dimensional Euclidean Space ◽  
Mathematical Methods ◽  
Analytic Number ◽  
Fundamental Theorems

There are many uses of Fourier analysis in the analytic number theory. In this paper we shall derive two fundamental theorems using Cramer’s method (Mathematical methods of statistics, 1946). Let E, E* be unit cubes in the whole n-dimensional Euclidean space X such that

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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