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

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.

### 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
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### References:

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