Some problems of Analytic number theory IV

R Balasubramanian (1) , K Ramachandra (2)

1 IMSc - Institute of Mathematical Sciences [Chennai]
2 TIFR - Tata Institute for Fundamental Research

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 ${\rm Exp\,Exp}((\zeta(s))^{\frac{1}{2}})$.

Mots clés: asymptotic formula for the summatory function of the coefficients of generating functions; $\Omega$-theorems; kernel function

Domaines: Mathématiques [math]

R Balasubramanian, K Ramachandra. Some problems of Analytic number theory IV. Hardy-Ramanujan Journal, 2002, Volume 25 - 2002, pp.5-21. ⟨10.46298/hrj.2002.145⟩. ⟨hal-01109802⟩