Journal of the Ramanujan Mathematical Society
Volume 40, Issue 4, December 2025 pp. 395–403.
An asymptotic expansion of the constant term of an automorphic function
Authors:
Babita, Abhash Kumar Jha, Bibekananda Maji and Manidipa Pal
Author institution:Department of Mathematical Sciences, Indian Institute of Technology (Banaras Hindu University), Varanasi 221 005,
Uttar Pradesh, India.
Summary:
Zagier, in 1981, conjectured that the constant term of the automorphic function y{12}|Δ(z)|{2} has an asymptotic
expansion in terms of the non-trivial zeros of Riemann zeta function. This was proved by Hafner and Stopple,
and later extended by Chakraborty, Kanemitsu and Maji. In this paper, we study the constant term of a general automorphic
function and there by extend the work of Chakraborty et al.
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