R Balasubramanian ; K Ramachandra - Some problems of Analytic number theory IV

hrj:145 - Hardy-Ramanujan Journal, January 1, 2002, Volume 25 - 2002 - https://doi.org/10.46298/hrj.2002.145
Some problems of Analytic number theory IV

Authors: R Balasubramanian ; K Ramachandra

In the present paper, we use Ramachandra's kernel function of the second order, namely ${\rm Exp} ((\sin z)^2)$, which has some advantages over the earlier kernel ${\rm Exp} (z^{4a+2})$ where $a$ is a positive integer. As an outcome of the new kernel we are able to handle $\Omega$-theorems for error terms in the asymptotic formula for the summatory function of the coefficients of generating functions of the ${\rm Exp}(\zeta(s)), {\rm Exp\,Exp}(\zeta(s))$ and also of the type ${\rm Exp\,Exp}((\zeta(s))^{\frac{1}{2}})$.


Volume: Volume 25 - 2002
Published on: January 1, 2002
Imported on: March 3, 2015
Keywords: asymptotic formula for the summatory function of the coefficients of generating functions, $\Omega$-theorems,kernel function,[MATH] Mathematics [math]


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