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 Corrigenda

1931 ◽  
Vol 27 (1) ◽  
pp. 25-25
Keyword(s):  
Fourier Series ◽  
Analytic Continuation ◽  
Analytic Theory ◽  
Theory Of Numbers

Some applications of Fourier series in the analytic theory of numbers.Page 589, equation (3–10), after “k>0” insert “and 0<R(s)< 1,” and for “2nπi/k” read “2nπix/k.”Page 589, equation (3·11), forAdd also ‘The evaluation of the integrals given in (3·11) is obvious when 0 < R (s) < 1, and then holds also for 0 < R (s) < 2 by the theory of analytic continuation.”

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