Vector-valued modular forms and Poincaré series

By M. Knopp, Geoffrey Mason. 2004

87 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bc2b268c67c4e8167b0c5a21e5f4374fcdd85b6a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. F. Pellarin
2. C. Franc
3. Christopher Marks
4. Geoffrey Mason
5. Siu-Hung Ng

In Geometry and Topology

1. F. Pellarin
2. C. Franc
3. Christopher Marks
4. Geoffrey Mason
5. Siu-Hung Ng
6. Bruno Anglès

In Mathematical Physics

1. F. Pellarin
2. C. Franc
3. Christopher Marks
4. Geoffrey Mason
5. Siu-Hung Ng

Citations in the corpus

• Hypergeometric series, modular linear differential equations and vector-valued modular forms (2015, background): “Among other things, in [24] the authors show that Hk(ρ) is finite-dimensional, and that Hk(ρ) = 0 if k < −2α where α is as in Theorem 3.”
• Values of certain L-series in positive characteristic (2011, methodology): “The following definition is a simple adaptation of the notion of vectorial modular form for SL2(Z) investigated in works by Knopp and Mason such as [13, 15], the most relevant for us.”
• Structure of the module of vector‐valued modular forms (2009, background): “2 of [5], we can find, for large enough k, a (meromorphic) vector-valued modular form Pr(τ) of weight k such that the component functions Pr,j(τ) are as follows: Pr,r(τ) = qrr + .”