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Article: On divisors of modular forms
Title | On divisors of modular forms |
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Authors | |
Issue Date | 2018 |
Citation | Advances in Mathematics, 2018, v. 329, p. 541-554 How to Cite? |
Abstract | The denominator formula for the Monster Lie algebra is the product expansion for the modular function $J(z)−J(τ)$ given in terms of the Hecke system of $SL_2(Z)$-modular functions $j_n(τ)$. It is prominent in Zagier’s seminal paper on traces of singular moduli, and in the Duncan-Frenkel work on Moonshine. The formula is equivalent to the description of the generating function for the $j_n(z)$ as a weight 2 modular form with a pole at z. Although these results rely on the fact that $X_0(1)$ has genus 0, here we obtain a generalization, framed in terms of polar harmonic Maass forms, for all of the $X_0(N)$ modular curves. We use these functions to study divisors of modular forms. |
Persistent Identifier | http://hdl.handle.net/10722/251433 |
DC Field | Value | Language |
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dc.contributor.author | Bringmann, K | - |
dc.contributor.author | Kane, BR | - |
dc.contributor.author | Löbrich, S | - |
dc.contributor.author | Ono, K | - |
dc.contributor.author | Rolen, L | - |
dc.date.accessioned | 2018-03-01T03:39:13Z | - |
dc.date.available | 2018-03-01T03:39:13Z | - |
dc.date.issued | 2018 | - |
dc.identifier.citation | Advances in Mathematics, 2018, v. 329, p. 541-554 | - |
dc.identifier.uri | http://hdl.handle.net/10722/251433 | - |
dc.description.abstract | The denominator formula for the Monster Lie algebra is the product expansion for the modular function $J(z)−J(τ)$ given in terms of the Hecke system of $SL_2(Z)$-modular functions $j_n(τ)$. It is prominent in Zagier’s seminal paper on traces of singular moduli, and in the Duncan-Frenkel work on Moonshine. The formula is equivalent to the description of the generating function for the $j_n(z)$ as a weight 2 modular form with a pole at z. Although these results rely on the fact that $X_0(1)$ has genus 0, here we obtain a generalization, framed in terms of polar harmonic Maass forms, for all of the $X_0(N)$ modular curves. We use these functions to study divisors of modular forms. | - |
dc.language | eng | - |
dc.relation.ispartof | Advances in Mathematics | - |
dc.title | On divisors of modular forms | - |
dc.type | Article | - |
dc.identifier.email | Kane, BR: bkane@hku.hk | - |
dc.identifier.authority | Kane, BR=rp01820 | - |
dc.description.nature | postprint | - |
dc.identifier.hkuros | 284249 | - |
dc.identifier.volume | 329 | - |
dc.identifier.spage | 541 | - |
dc.identifier.epage | 554 | - |