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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Riemann-Siegel integral formula for the Lerch zeta function


Authors: Eugenio P. Balanzario and Jorge Sánchez-Ortiz
Journal: Math. Comp. 81 (2012), 2319-2333
MSC (2010): Primary 11M35
Published electronically: November 29, 2011
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Abstract: Here we present a Riemann-Siegel integral formula for the Lerch zeta function. Proceeding as in Turing's method for computing the Riemann zeta function, our integral formula allows for the numerical computation of the Lerch zeta function by numerical quadratures.


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Additional Information

Eugenio P. Balanzario
Affiliation: Instituto de Matemáticas, Unidad Morelia, Universidad Nacional Autónoma de México
Email: ebg@matmor.unam.mx

Jorge Sánchez-Ortiz
Affiliation: Apartado Postal 61-3 (Xangari), 58089, Morelia Michoacán, México
Address at time of publication: Facultad de Matemáticas, Av. Lázaro Cárdenas S/N, Ciudad Universitaria, Chilpancingo Gro., México
Email: jsanchez@matmor.unam.mx

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02566-4
PII: S 0025-5718(2011)02566-4
Keywords: Lerch zeta function, Riemann-Siegel, saddle point
Received by editor(s): September 27, 2010
Received by editor(s) in revised form: April 15, 2011
Published electronically: November 29, 2011
Article copyright: © Copyright 2011 American Mathematical Society