The circle method and bounds for $L$-functions - I

Details The circle method and bounds for $L$-functions - I The circle method and bounds for $L$-functions - I

2012-02-18

arxiv.org/abs/1202.4068v1

Mathematics

Number Theory

8 pages

Scientific paper

Let $f$ be a Hecke-Maass or holomorphic primitive cusp form of arbitrary level and nebentypus, and let $\chi$ be a primitive character of conductor $M$. For the twisted $L$-function $L(s,f\otimes \chi)$ we establish the hybrid subconvex bound $$ L(1/2+it,f\otimes\chi)\ll (M(3+|t|))^{1/2-1/18+\varepsilon}, $$ for $t\in \mathbb R$. The implied constant depends only on the form $f$ and $\varepsilon$.

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