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Publication - Professor Andrew Booker

    A conjectural extension of Hecke’s converse theorem


    Bettin, S, Bober, J, Booker, A, Conrey, B, Lee, M, Molteni, G, Oliver, T, Platt, DJ & Steiner, R, 2018, ‘A conjectural extension of Hecke’s converse theorem’. Ramanujan Journal, vol 47., pp. 659-684


    We formulate a precise conjecture that, if true, extends the converse theorem of Hecke without requiring hypotheses on twists by Dirichlet characters or an Euler product. The main idea is to linearize the Euler product, replacing it by twists by Ramanujan sums. We provide evidence for the conjecture, including proofs of some special cases and under various additional hypotheses.

    Full details in the University publications repository