Computing an order complete basis for M^∞(N) and Applications

2019/07/01 by van Hoeij, Mark, Radu, Cristian-Silviu
#11F03 #11P83 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1907.01057

Abstract

This paper gives a quick way to construct all modular functions for the group Γ₀(N) having only a pole at τ= i ∞. We assume that we are given two modular functions f,g for Γ₀(N) with poles only at i ∞ and coprime pole orders. As an application we obtain two new identities from which one can derive that p(11n+6)≡ 0\pmod11, here p(n) is the usual partition function.

Related

• Structure and bases of modular space sequences (M_2k(Γ₀(N)))_{k∈ ℕ^*} and (S_2k(Γ₀(N)))_{k∈ ℕ^*}. Part I : Strong modular units
• Structure and bases of modular space sequences (M_2k(Γ₀(N)))_{k∈ ℕ^*} and (S_2k(Γ₀(N)))_{k∈ ℕ^*}. Part II: a modular butterfly hunt
• Congruences for coefficients of modular functions in levels 3, 5, and 7\n with poles at 0
• Congruences modulo powers of 11 for some eta-quotients
• Generators of the group of modular units for Gamma1(N) over the rationals