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While rotation has a major impact on stellar structure and evolution, its effects are not well understood. Thanks to high-quality and long-time base photometric observations obtained with recent space missions, we are now able to study stellar rotation more precisely.<\/jats:p><jats:p><jats:italic>Aims<\/jats:italic>. We aim to constrain radial differential rotation profiles in<jats:italic>\u03b3<\/jats:italic>Doradus (<jats:italic>\u03b3<\/jats:italic>Dor) stars, and to develop new theoretical seismic diagnosis for such stars with rapid and potentially non-uniform rotation.<\/jats:p><jats:p><jats:italic>Methods<\/jats:italic>. We have derived a new asymptotic description which accounts for the impact of weak differential near-core rotation on gravity-mode period spacings. The theoretical predictions are illustrated from pulsation computations with the code GYRE and compared with observations of<jats:italic>\u03b3<\/jats:italic>Dor stars. When possible, we also derived the surface rotation rates in these stars by detecting and analysing signatures of rotational modulation, and computed the core-to-surface rotation ratios.<\/jats:p><jats:p><jats:italic>Results<\/jats:italic>. Stellar rotation must be strongly differential before its effects on period spacing patterns can be detected, unless multiple period spacing patterns can be compared. Six stars in our sample exhibit a single unexplained period spacing pattern of retrograde modes. We hypothesise that these are Yanai modes. Finally, we find signatures of rotational spot modulation in the photometric data of eight targets.<\/jats:p><jats:p><jats:italic>Conclusions<\/jats:italic>. If only one period spacing pattern is detected and analysed for a star, it is difficult to detect differential rotation. A rigidly rotating model will often provide the best solution. Differential rotation can only be detected when multiple period spacing patterns have been found for a single star or its surface rotation rate is known as well. This is the case for eight of the stars in our sample, revealing surface-to-core rotation ratios between 0.95 and 1.05.<\/jats:p>","DOI":"10.1051\/0004-6361\/201832718","type":"journal-article","created":{"date-parts":[[2018,7,30]],"date-time":"2018-07-30T18:45:04Z","timestamp":1532976304000},"page":"A24","source":"Crossref","is-referenced-by-count":109,"title":["Sensitivity of gravito-inertial modes to differential rotation in intermediate-mass main-sequence stars"],"prefix":"10.1051","volume":"618","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2771-1745","authenticated-orcid":false,"given":"T.","family":"Van Reeth","sequence":"first","affiliation":[]},{"given":"J. S. 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