Matches in SemOpenAlex for { <https://semopenalex.org/work/W2908969280> ?p ?o ?g. }
- W2908969280 abstract "We show that as $Tto infty$, for all $tin [T,2T]$ outside of a set of measure $mathrm{o}(T)$, $$ int_{-(log T)^{theta}}^{(log T)^{theta}} |zeta(tfrac 12 + mathrm{i} t + mathrm{i} h)|^{beta} mathrm{d} h = (log T)^{f_{theta}(beta) + mathrm{o}(1)}, $$ for some explicit exponent $f_{theta}(beta)$, where $theta > -1$ and $beta > 0$. This proves an extended version of a conjecture of Fyodorov and Keating (2014). In particular, it shows that, for all $theta > -1$, the moments exhibit a phase transition at a critical exponent $beta_c(theta)$, below which $f_theta(beta)$ is quadratic and above which $f_theta(beta)$ is linear. The form of the exponent $f_theta$ also differs between mesoscopic intervals ($-1<theta<0$) and macroscopic intervals ($theta>0$), a phenomenon that stems from an approximate tree structure for the correlations of zeta. We also prove that, for all $tin [T,2T]$ outside a set of measure $mathrm{o}(T)$, $$ max_{|h| leq (log T)^{theta}} |zeta(tfrac{1}{2} + mathrm{i} t + mathrm{i} h)| = (log T)^{m(theta) + mathrm{o}(1)}, $$ for some explicit $m(theta)$. This generalizes earlier results of Najnudel (2018) and Arguin et al. (2019) for $theta = 0$. The proofs are unconditional, except for the upper bounds when $theta > 3$, where the Riemann hypothesis is assumed." @default.
- W2908969280 created "2019-01-25" @default.
- W2908969280 creator A5010318685 @default.
- W2908969280 creator A5027276960 @default.
- W2908969280 creator A5046144341 @default.
- W2908969280 date "2021-11-01" @default.
- W2908969280 modified "2023-09-26" @default.
- W2908969280 title "Moments of the Riemann zeta function on short intervals of the critical line" @default.
- W2908969280 cites W1569502688 @default.
- W2908969280 cites W1592212038 @default.
- W2908969280 cites W1862662845 @default.
- W2908969280 cites W1967457180 @default.
- W2908969280 cites W1972962012 @default.
- W2908969280 cites W1973766190 @default.
- W2908969280 cites W1986386529 @default.
- W2908969280 cites W1986417812 @default.
- W2908969280 cites W2001729983 @default.
- W2908969280 cites W2005036050 @default.
- W2908969280 cites W2056183459 @default.
- W2908969280 cites W2067941652 @default.
- W2908969280 cites W2083715726 @default.
- W2908969280 cites W2095393613 @default.
- W2908969280 cites W2121902984 @default.
- W2908969280 cites W2134478378 @default.
- W2908969280 cites W2156948039 @default.
- W2908969280 cites W2169254136 @default.
- W2908969280 cites W2327211522 @default.
- W2908969280 cites W2499078703 @default.
- W2908969280 cites W2796187088 @default.
- W2908969280 cites W2884112638 @default.
- W2908969280 cites W2962707111 @default.
- W2908969280 cites W2962718946 @default.
- W2908969280 cites W2962912576 @default.
- W2908969280 cites W2962996535 @default.
- W2908969280 cites W2963106368 @default.
- W2908969280 cites W2963237125 @default.
- W2908969280 cites W2963599794 @default.
- W2908969280 cites W2976790204 @default.
- W2908969280 cites W3009018969 @default.
- W2908969280 cites W3016856812 @default.
- W2908969280 cites W3093543361 @default.
- W2908969280 cites W3099592725 @default.
- W2908969280 cites W3100405748 @default.
- W2908969280 cites W3102200383 @default.
- W2908969280 cites W3102602540 @default.
- W2908969280 cites W3102853182 @default.
- W2908969280 cites W3104709962 @default.
- W2908969280 cites W3105844307 @default.
- W2908969280 cites W3106435960 @default.
- W2908969280 cites W3121187802 @default.
- W2908969280 cites W4248497354 @default.
- W2908969280 cites W4254010946 @default.
- W2908969280 doi "https://doi.org/10.1214/21-aop1524" @default.
- W2908969280 hasPublicationYear "2021" @default.
- W2908969280 type Work @default.
- W2908969280 sameAs 2908969280 @default.
- W2908969280 citedByCount "13" @default.
- W2908969280 countsByYear W29089692802019 @default.
- W2908969280 countsByYear W29089692802020 @default.
- W2908969280 countsByYear W29089692802021 @default.
- W2908969280 countsByYear W29089692802022 @default.
- W2908969280 countsByYear W29089692802023 @default.
- W2908969280 crossrefType "journal-article" @default.
- W2908969280 hasAuthorship W2908969280A5010318685 @default.
- W2908969280 hasAuthorship W2908969280A5027276960 @default.
- W2908969280 hasAuthorship W2908969280A5046144341 @default.
- W2908969280 hasBestOaLocation W29089692802 @default.
- W2908969280 hasConcept C114614502 @default.
- W2908969280 hasConcept C134306372 @default.
- W2908969280 hasConcept C138885662 @default.
- W2908969280 hasConcept C199479865 @default.
- W2908969280 hasConcept C2780388253 @default.
- W2908969280 hasConcept C2780990831 @default.
- W2908969280 hasConcept C33923547 @default.
- W2908969280 hasConcept C35235930 @default.
- W2908969280 hasConcept C37914503 @default.
- W2908969280 hasConcept C41895202 @default.
- W2908969280 hasConceptScore W2908969280C114614502 @default.
- W2908969280 hasConceptScore W2908969280C134306372 @default.
- W2908969280 hasConceptScore W2908969280C138885662 @default.
- W2908969280 hasConceptScore W2908969280C199479865 @default.
- W2908969280 hasConceptScore W2908969280C2780388253 @default.
- W2908969280 hasConceptScore W2908969280C2780990831 @default.
- W2908969280 hasConceptScore W2908969280C33923547 @default.
- W2908969280 hasConceptScore W2908969280C35235930 @default.
- W2908969280 hasConceptScore W2908969280C37914503 @default.
- W2908969280 hasConceptScore W2908969280C41895202 @default.
- W2908969280 hasIssue "6" @default.
- W2908969280 hasLocation W29089692801 @default.
- W2908969280 hasLocation W29089692802 @default.
- W2908969280 hasLocation W29089692803 @default.
- W2908969280 hasOpenAccess W2908969280 @default.
- W2908969280 hasPrimaryLocation W29089692801 @default.
- W2908969280 hasRelatedWork W1991418287 @default.
- W2908969280 hasRelatedWork W2013205609 @default.
- W2908969280 hasRelatedWork W2417611065 @default.
- W2908969280 hasRelatedWork W2949343084 @default.
- W2908969280 hasRelatedWork W2952184424 @default.
- W2908969280 hasRelatedWork W2952714087 @default.
- W2908969280 hasRelatedWork W2991008008 @default.