{"docId":145,"paperId":145,"url":"https:\/\/hrj.episciences.org\/145","doi":"10.46298\/hrj.2002.145","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":36,"name":"Volume 25 - 2002"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01109802","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01109802v1","dateSubmitted":"2015-03-03 16:13:54","dateAccepted":"2015-06-12 16:05:45","datePublished":"2002-01-01 08:00:00","titles":{"en":"Some problems of Analytic number theory IV"},"authors":["Balasubramanian, R","Ramachandra, K"],"abstracts":{"en":"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 ${\\rm Exp\\,Exp}((\\zeta(s))^{\\frac{1}{2}})$."},"keywords":[{"en":" asymptotic formula for the summatory function of the coefficients of generating functions"},{"en":" $\\Omega$-theorems"},{"en":"kernel function"},"[MATH] Mathematics [math]"]}