Zeta-functions of ideal classes in quadratic fields and their zeros on the critical line

1968 ◽  
Vol 43 (1) ◽  
pp. 18-30 ◽  
Author(s):  
K. Chandrasekharan ◽  
Raghavan Narasimhan
Keyword(s):  
Critical Line ◽  
Zeta Functions ◽  
Quadratic Fields

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 Zeros of quadratic zeta-functions on the critical line

1995 ◽  
Vol 69 (1) ◽  
pp. 21-38 ◽  
Author(s):  
A. Sankaranarayanan
Keyword(s):  
Critical Line ◽  
Zeta Functions

scholarly journals On complex zeros off the critical line for non-monomial polynomial of zeta-functions

2016 ◽  
Vol 284 (1-2) ◽  
pp. 23-39 ◽  
Author(s):  
Takashi Nakamura ◽  
Łukasz Pańkowski
Keyword(s):  
Critical Line ◽  
Zeta Functions ◽  
Complex Zeros

scholarly journals Similar Sublattices of Planar Lattices

2011 ◽  
Vol 63 (6) ◽  
pp. 1220-1537 ◽  
Author(s):  
Michael Baake ◽  
Rudolf Scharlau ◽  
Peter Zeiner
Keyword(s):  
Dirichlet Series ◽  
Generating Functions ◽  
Quadratic Field ◽  
Zeta Functions ◽  
Imaginary Quadratic Field ◽  
Quadratic Fields ◽  
Imaginary Quadratic Fields ◽  
Planar Lattice ◽  
Planar Lattices

AbstractThe similar sublattices of a planar lattice can be classified via its multiplier ring. The latter is the ring of rational integers in the generic case, and an order in an imaginary quadratic field otherwise. Several classes of examples are discussed, with special emphasis on concrete results. In particular, we derive Dirichlet series generating functions for the number of distinct similar sublattices of a given index, and relate them to zeta functions of orders in imaginary quadratic fields.

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