ON THE ASYMPTOTIC FORMULA FOR THE FOURIER COEFFICIENTS OF THE <b><i>j</i></b>-FUNCTION

M. Ram Murty, Kannappan Sampath

Type: Article

Publication Date: 2016-01-01

Citations: 1

DOI: https://doi.org/10.2206/kyushujm.70.083

Abstract

We derive the asymptotic formula for the Fourier coefficients of the j-function using an arithmetic formula given by Kaneko based on Zagier's work on the traces of singular moduli. The key ingredient along with the Kaneko-Zagier formula is Laplace's method.

Locations

Kyushu Journal of Mathematics - View - PDF

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+ PDF Chat	Primes of the form x<sup>2 </sup>+ ny<sup>2</sup>	2012	K. Raja Rama Gandhi
+	Quadratic Irrationals: An Introduction to Classical Number Theory	2013	Franz Halter‐Koch
+	A Course in Arithmetic	1973	Jean Pierre Serre
+	Traces of singular moduli	2002	Don Zagier
+	AN ASYMPTOTIC FORMULA FOR THE COEFFICIENTS OF j(z)	2012	Michael Dewar M. Ram Murty
+	Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms	2013	Jan Hendrik Bruinier Ken Ono
+ PDF Chat	Über die Entwicklungskoeffizienten der automorphen Formen	1932	Hans Petersson
+ PDF Chat	Asymptotic Formulaae in Combinatory Analysis	1918	G. H. Hardy S. Ramanujan
+	ASYMPTOTIC APPROXIMATIONS TO INTEGRALS	1980
+	Traces of singular moduli and the Fourier coefficients of the elliptic modular function j（T）.	1999	Masanobu Kaneko

ON THE ASYMPTOTIC FORMULA FOR THE FOURIER COEFFICIENTS OF THE &lt;b&gt;&lt;i&gt;j&lt;/i&gt;&lt;/b&gt;-FUNCTION