# Weakly holomorphic modular forms on $$\Gamma _{0}(4)$$ Γ 0 ( 4 ) and Borcherds products on unitary group $$\mathrm{U}(2,1)$$ U ( 2 , 1 )

Weakly holomorphic modular forms on $$\Gamma _{0}(4)$$ Γ 0 ( 4 ) and Borcherds... In this note, we construct canonical bases for the spaces of weakly holomorphic modular forms with poles supported at the cusp $$\infty$$ ∞ for $$\Gamma _{0}(4)$$ Γ 0 ( 4 ) of integral weight k for $$k\le -1$$ k ≤ - 1 , and we make use of the basis elements for the case $$k=-1$$ k = - 1 to construct explicit Borcherds products on unitary group $$\mathrm{U}(2,1)$$ U ( 2 , 1 ) . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in Number Theory Springer Journals

# Weakly holomorphic modular forms on $$\Gamma _{0}(4)$$ Γ 0 ( 4 ) and Borcherds products on unitary group $$\mathrm{U}(2,1)$$ U ( 2 , 1 )

, Volume 4 (1) – Jan 31, 2018
25 pages

/lp/springer_journal/weakly-holomorphic-modular-forms-on-gamma-0-4-0-4-and-borcherds-yCDuQSC0pj
Publisher
Springer International Publishing
Subject
Mathematics; Number Theory
eISSN
2363-9555
D.O.I.
10.1007/s40993-018-0096-z
Publisher site
See Article on Publisher Site

### Abstract

In this note, we construct canonical bases for the spaces of weakly holomorphic modular forms with poles supported at the cusp $$\infty$$ ∞ for $$\Gamma _{0}(4)$$ Γ 0 ( 4 ) of integral weight k for $$k\le -1$$ k ≤ - 1 , and we make use of the basis elements for the case $$k=-1$$ k = - 1 to construct explicit Borcherds products on unitary group $$\mathrm{U}(2,1)$$ U ( 2 , 1 ) .

### Journal

Research in Number TheorySpringer Journals

Published: Jan 31, 2018

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