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A case of simultaneous non-vanishing of automorphic $L$-functions

Volume 182 / 2018

Ritabrata Munshi, Jyoti Sengupta Acta Arithmetica 182 (2018), 1-11 MSC: Primary 11F67; Secondary 11F11, 11F66. DOI: 10.4064/aa8179-9-2017 Published online: 18 December 2017

Abstract

We show that for $k\geq 12$ even, there exists an effectively computable constant $q_k$ such that for any prime $q \gt q_k$, there exists a newform $f$ of weight $k$ and level $q$ such that $$ L(1/2,f)L(1/2,\mathop{\rm Sym}\nolimits^2 f)\neq 0. $$

Authors

  • Ritabrata MunshiSchool of Mathematics
    Tata Institute of Fundamental Research
    1 Dr. Homi Bhabha Road
    Colaba, Mumbai 400005, India
    and
    Indian Statistical Institute
    203 B.T. Road
    Kolkata 700108, India
    e-mail
  • Jyoti SenguptaSchool of Mathematics
    Tata Institute of Fundamental Research
    1 Dr. Homi Bhabha Road
    Colaba, Mumbai 400005, India
    e-mail

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