Rational Period Functions and Cycle Integrals

  title={Rational Period Functions and Cycle Integrals},
  author={William Duke and {\"O}zlem Imamoḡlu and {\'A}rpad T{\'o}th},
The existence of such a basis is well-known, and our aim here is to illustrate the effectiveness of using weakly holomorphic forms in providing one. Our main goal is to construct modular integrals for certain rational solutions ψ to (1) for any k ∈ Z made out of indefinite binary quadratic forms. A modular integral for ψ is a periodic function F holomorphic on the upper half-plane H and meromorphic at i∞ that satisfies