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A class of non-holomorphic modular forms I

Abstract:

This paper studies examples of real analytic functions on the upper half plane satisfying a modular transformation property of the form

(0.1) f(az + b/cz + d)= (cz + d)^r (cz + d)^s f(z)

for integers r, s. They do not satisfy a simple condition involving the Laplacian. The raison d’être for this class of functions is two-fold:

(1) Holomorphic modular forms f with rational Fourier coefficients correspond to certain pure motives Mf over Q. Using iterated integrals, we c...

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Publication status:
Published
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS Division
Department:
Mathematical Institute
Oxford college:
All Souls College
Publisher:
Springer Publisher's website
Journal:
Research in the Mathematical Sciences Journal website
Publication date:
2018-01-05
Acceptance date:
2017-12-18
EISSN:
2197-9847
Pubs id:
pubs:815377
URN:
uri:d37aa066-28fb-49c7-8bf1-3c448142359e
UUID:
uuid:d37aa066-28fb-49c7-8bf1-3c448142359e
Local pid:
pubs:815377

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