An exact formula for a Lambert series associated to a cusp form and the Möbius function

In 1981, Zagier conjectured that the constant term of the automorphic form y 12 | Δ ( z ) | 2 , that is, a 0 ( y ) : = y 12 ∑ n = 1 ∞ τ 2 ( n ) exp ( - 4 π n y ) , where τ ( n ) is the n th Fourier coefficient of the Ramanujan cusp form Δ ( z ) , has an asymptotic expansion when y → 0 + and it can b...

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Veröffentlicht in:	The Ramanujan journal 2022-02, Vol.57 (2), p.769-784
Hauptverfasser:	Juyal, Abhishek, Maji, Bibekananda, Sathyanarayana, Sumukha
Format:	Artikel
Sprache:	eng
Schlagworte:	Asymptotic series Combinatorics Cusps Field Theory and Polynomials Fourier Analysis Fourier series Functions of a Complex Variable Infinite series Mathematics Mathematics and Statistics Number Theory
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