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Determination of ${\bf GL}(2)$ Maass forms from twists in the level aspect

Volume 189 / 2019

Biswajyoti Saha, Jyoti Sengupta Acta Arithmetica 189 (2019), 165-178 MSC: 11F67, 11F11, 11F66. DOI: 10.4064/aa180314-2-9 Published online: 10 May 2019

Abstract

We address the problem of determining a ${\bf GL}(2)$ Maass cusp form (of weight zero) from the central values of the Rankin–Selberg $L$-functions $L(1/2,f\otimes u_j)$ for infinitely many primes $p$ and all the normalised Maass cusp forms $u_j$ which are newforms for $\varGamma_0(p)$. This generalises Luo’s result on determining holomorphic cuspidal newforms.

Authors

  • Biswajyoti SahaSchool of Mathematics
    Tata Institute of Fundamental Research
    Dr. Homi Bhabha Road, Navy Nagar
    Mumbai 400005, India
    and
    School of Mathematics and Statistics
    University of Hyderabad
    Prof. C. R. Rao Road
    Hyderabad 500046, India
    e-mail
    e-mail
  • Jyoti SenguptaSchool of Mathematics
    Tata Institute of Fundamental Research
    Dr. Homi Bhabha Road, Navy Nagar
    Mumbai 400005, India
    e-mail

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