An Approximate Functional Equation for the Primitive of Hardy’s Function

2017 ◽  
Vol 299 (1) ◽  
pp. 109-116
Author(s):  
Matti Jutila
Keyword(s):  
Functional Equation ◽  
Approximate Functional Equation ◽  
Hardy’S Function

scholarly journals Evaluating -functions with few known coefficients

2014 ◽  
Vol 17 (1) ◽  
pp. 245-258 ◽  
Author(s):  
David W. Farmer ◽  
Nathan C. Ryan
Keyword(s):  
Functional Equation ◽  
Computational Effort ◽  
Standard Approach ◽  
Approximate Functional Equation

AbstractWe address the problem of evaluating an $L$-function when only a small number of its Dirichlet coefficients are known. We use the approximate functional equation in a new way and find that it is possible to evaluate the $L$-function more precisely than one would expect from the standard approach. The method, however, requires considerably more computational effort to achieve a given accuracy than would be needed if more Dirichlet coefficients were available.

Approximate Functional Equation

2003 ◽  
pp. 53-69
Author(s):  
Antanas Laurinčikas ◽  
Ramūnas Garunkštis
Keyword(s):  
Functional Equation ◽  
Approximate Functional Equation

An approximate functional equation for Dirichlet L -functions

1965 ◽  
Vol 284 (1397) ◽  
pp. 224-236 ◽  
Keyword(s):  
Functional Equation ◽  
Asymptotic Formula ◽  
Royal Society ◽  
Approximate Functional Equation

A new asymptotic formula is derived for the computation of Dirichlet L -functions, L ( s , X ), where s = σ + i t . The formula is applicable for large values of t and it has been used on the Mercury computer at Manchester University to calculate the zeros of the L -functions with moduli 3 and 4 on the line Rs = ½. The results have been placed in the Royal Society Depository for Unpublished Mathematical Tables (no. 83).

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