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The Quarterly Journal of Mathematics Advance Access published online on August 3, 2007
The Quarterly Journal of Mathematics, doi:10.1093/qmath/ham027
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© 2007. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

ON A LIMITING RELATION BETWEEN RAMANUJAN'S ENTIRE FUNCTION Aq(z) AND {theta}-FUNCTIONS

Ruiming Zhang{dagger}

Binzhou Vocational College, 533 Bohai 9 Road, Binzhou City, Shandong 256624, People's Republic of China

{dagger} E-mail: ruimingzhang{at}yahoo.com

Received 25 August 2006; revised 23 April 2007
  Abstract

We will use a discrete analogue of the classical Laplace method to show that the main term of the asymptotic expansions of certain entire functions, including Ramanujan's entire function Aq(z), can be expressed in terms of {theta}-functions.

Current address: School of Mathematics, Guangxi Normal University, Guilin City, Guangxi 541004, People's Republic of China.


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