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2 results

8 - Modular derivatives and vector-valued modular forms
from Part I - Modular forms and their variants
Eric D'Hoker, University of California, Los Angeles, Justin Kaidi, Kyushu University
Book:

Modular Forms and String Theory

Published online:

28 November 2024

Print publication:

12 December 2024, pp 155-167
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Summary

In this chapter, we construct differential equations in the modular parameter and find solutions to these equations in simple cases. The solutions can generically be assembled into vector-valued modular forms, which have proven fruitful in recent works in mathematics and physics. We will establish that, in general, each component of a vector-valued modular form is a modular form for a congruence subgroup.

Results on the non-vanishing of derivatives of L-functions of vector-valued modular forms
Part of
- Discontinuous groups and automorphic forms
Subong Lim, Wissam Raji
Journal:

Proceedings of the Edinburgh Mathematical Society , First View

Published online by Cambridge University Press:

21 November 2024, pp. 1-17
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We prove the existence of a vector-valued cusp form for the full modular group for which the nth derivative of its L-function does not vanish under certain conditions. As an application, we generalize our result to Kohnen’s plus space and prove an analogous result for Jacobi forms.

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2 results

8 - Modular derivatives and vector-valued modular forms

Summary

Results on the non-vanishing of derivatives of L-functions of vector-valued modular forms