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Asymptotic formulae.

Jakimczuk, Rafael (2004)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Asymptotic formulae for partition ranks

Jehanne Dousse, Michael H. Mertens (2015)

Acta Arithmetica

Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F. Dyson and recently proved by the first author and K. Bringmann.

Asymptotic formulas for the coefficients of certain automorphic functions

Jaban Meher, Karam Deo Shankhadhar (2015)

Acta Arithmetica

We derive asymptotic formulas for the coefficients of certain classes of weakly holomorphic Jacobi forms and weakly holomorphic modular forms (not necessarily of integral weight) without using the circle method. Then two applications of these formulas are given. Namely, we estimate the growth of the Fourier coefficients of two important weak Jacobi forms of index 1 and non-positive weights and obtain an asymptotic formula for the Fourier coefficients of the modular functions θ k / η l for all integers k,l...

Asymptotic nature of higher Mahler measure

(2014)

Acta Arithmetica

We consider Akatsuka’s zeta Mahler measure as a generating function of the higher Mahler measure m k ( P ) of a polynomial P , where m k ( P ) is the integral of l o g k | P | over the complex unit circle. Restricting ourselves to P(x) = x - r with |r| = 1 we show some new asymptotic results regarding m k ( P ) , in particular | m k ( P ) | / k ! 1 / π as k → ∞.

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