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Maaß-Shimura operator. Consider the operator Sk: f(z) → f(z) d 2 1/2 (+28(²)) + 2-1(²) k 2πi 2iI(z) dz Suppose that f(z) is weakly modular of weight k and show that dk fis invariant for the weight k + 2 action of SL₂(Z).

Maaß-Shimura operator. Consider the operator Sk: f(z) → f(z) d 2 1/2 (+28(²)) + 2-1(²) k 2πi 2iI(z) dz Suppose that f(z) is weakly modular of weight k and show that dk fis invariant for the weight k + 2 action of SL₂(Z).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Maaß-Shimura operator. Consider the operator d + dz 1 Sk : f(z) → 2Ti (k(2) 2iI(z) Suppose that f(2) is weakly modular of weight k and show that 8rf is invariant for the weight k + 2 action of SL2(Z).
Transcribed Image Text:Maaß-Shimura operator. Consider the operator d + dz 1 Sk : f(z) → 2Ti (k(2) 2iI(z) Suppose that f(2) is weakly modular of weight k and show that 8rf is invariant for the weight k + 2 action of SL2(Z).
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