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Munshi, Ritabrata; Singh, Saurabh Kumar

Weyl bound for \(p\)-power twist of \(\mathrm{GL}(2)L\)-functions. (English) Zbl 1461.11077

Algebra Number Theory 13, No. 6, 1395-1413 (2019).
Summary: Let \(f\) be a cuspidal eigenform (holomorphic or Maass) for the congruence group \(\Gamma_0(N)\) with \(N\) square-free. Let \(p\) be a prime and let \(\chi\) be a primitive character of modulus \(p^{3r}\). We shall prove the Weyl-type subconvex bound \[ L\bigl(\frac{1}{2}+it,f\otimes\chi\bigr)\ll_{f,t,\varepsilon}p^{r+\varepsilon}, \] where \(\varepsilon>0\) is any positive real number.

Cited in 4 Documents

MSC:

11F66 Langlands \(L\)-functions; one variable Dirichlet series and functional equations
11F37 Forms of half-integer weight; nonholomorphic modular forms
11M41 Other Dirichlet series and zeta functions

Keywords:

Maass forms; Hecke eigenforms; Voronoi summation formula; Poisson summation formula
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\textit{R. Munshi} and \textit{S. K. Singh}, Algebra Number Theory 13, No. 6, 1395--1413 (2019; Zbl 1461.11077)
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