Generalized modular forms including the weak Maass forms,the Ramanujan's Theta functions and the Tau function

2012/05/14 by Christian Pierre, Pierre, Christian
Mathematics · #11F11 #11F23 #11F30 #11F66 #11R39 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #math.GM #msc:11F11 #msc:11F23 #msc:11F30 #msc:11F66 #msc:11R39

paper · pdf · doi:10.48550/arxiv.1205.3485

67 pages

arxiv created 2012/05/14 · openalex publication_date 2012/05/14 · arxiv updated 2012/05/16 · openalex created_date 2022/08/28 · openalex updated_date 2026/07/28

Abstract

The modular forms are revisited from a geometric and an algebraic point of view leading to a geometric interpretation of the weak Maass forms connecting them to the Ramanujan Mock Theta functions and to the cusp forms generated from the Langlands global program.

Citations

• n-Dimensional global correspondences of Langlands over singular schemes (II)
• GL(2)-structures of the Langlands global program
• The Thurston's program derived from the Langlands global program with singularities
• Mock Theta Functions
• n-Dimensional global correspondences of Langlands
• The f(q) mock theta function conjecture and partition ranks
• The Final Problem : An Account of the Mock Theta Functions
• Dyson’s ranks and Maass forms
• The Langlands functoriality conjecture in the bisemialgebra framework
• On Modular Forms of Half Integral Weight

Related

• Mock Maass Forms Revisited
• Locally harmonic Maass forms and the kernel of the Shintani lift
• A class of non-holomorphic modular forms I
• A Unified Partial and Mock Theta Function
• On Kleinian mock modular forms