English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $f(z)$ be a holomorphic cusp form for the full modular group$SL_{2}(\mathbb{Z})$, and let $L(s,f)$ be the corresponding automorphic$L$-function associated to $f$. In this paper, we show that \begin{align*}N_{f}(\sigma,T)\ll T^{A(\sigma)(1-\sigma)+\varepsilon} \end{align*} with\begin{align*} A(\sigma)= \begin{cases} \frac{4}{4\sigma-1} &\textup{for}\ \\frac{21}{22}\leq\sigma \leq 1,\\ \frac{2}{13\sigma-11} &\textup{for}\ \\frac{17}{18}\leq\sigma\leq \frac{21}{22}, \end{cases} \end{align*}  where \begin{align*} N_{f}(\sigma,T):=\sum_{L(\beta+i\gamma,f)=0 \atop\sigma\leq\beta\leq1 ,\ 10\leq|\gamma|\leq T}1. \end{align*} When $\sigma$ isnear to 1, this improves the result of Ivi\'{c} \cite{I2} and gives a bestpossible estimate from the exhausted Weyl bounds. Moreover, such type resultscannot be obtained from the general results of Perelli \cite{P}.

On zero-density estimates of zeta-functions associated with Fourier coefficients of cusp forms