Congruences Concerning Values of the Modular Functions jn

Autor:	Gwynneth H. Coogan
Rok vydání:	2005
Předmět:	Pure mathematics symbols.namesake Algebra and Number Theory j-invariant Eisenstein series Modular form symbols Congruence relation Cusp form Modular curve Hecke operator Meromorphic function Mathematics
Zdroj:	The Ramanujan Journal. 10:43-50
ISSN:	1572-9303 1382-4090
DOI:	10.1007/s11139-005-3504-7
Popis:	The j-function j(z) = q−1+ 744 + 196884q + ⋅s plays an important role in many problems. In [7], Zagier, presented an interesting series of functions obtained from the j-function: j m (ζ) = (j(ζ) – 744)∨T0(m), where T0(m) is the usual m′th normalized weight 0 Hecke operator. In [3], Bruinier et al. show how this series of functions can be used to describe all meromorphic modular forms on SL2(ℤ). In this note we use these functions and basic notions about modular forms to determine previously unidentified congruence relations between the coefficients of Eisenstein series and the j-function.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e30d820258636c8a0697529be31564fc https://doi.org/10.1007/s11139-005-3504-7 Zobrazit plný text záznamu Full text from SpringerLink