Divisibility properties of coefficients of modular functions in genus zero levels
Divisibility properties of coefficients of modular functions in genus zero levels
We prove divisibility results for the Fourier coefficients of canonical basis elements for the spaces of weakly holomorphic modular forms of weight $0$ and levels $6, 10, 12, 18$ with poles only at the cusp at infinity. In addition, we show that these Fourier coefficients satisfy Zagier duality in all weights, and give a general formula for the generating functions of such canonical bases for all genus zero levels.
Modular and automorphic functions, Fourier coefficients of automorphic forms, spaces of weakly holomorphic modular forms, Mathematics - Number Theory, Fourier coefficients of canonical basis elements, FOS: Mathematics, divisibility, Number Theory (math.NT), Forms of half-integer weight; nonholomorphic modular forms, 11F03, 11F33, 11F37
Modular and automorphic functions, Fourier coefficients of automorphic forms, spaces of weakly holomorphic modular forms, Mathematics - Number Theory, Fourier coefficients of canonical basis elements, FOS: Mathematics, divisibility, Number Theory (math.NT), Forms of half-integer weight; nonholomorphic modular forms, 11F03, 11F33, 11F37
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