{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:29:22Z","timestamp":1760239762839,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,12,15]],"date-time":"2020-12-15T00:00:00Z","timestamp":1607990400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11971381, 11471258, 11701447"],"award-info":[{"award-number":["11971381, 11471258, 11701447"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Basic Research Program for Nature Science of Shaanxi Province","award":["2014JM1001, 2015KJXX-27"],"award-info":[{"award-number":["2014JM1001, 2015KJXX-27"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Let q&gt;2 be a prime, p be a given prime with p&lt;q. The main purpose of this paper is using transforms, the hybrid mean value of Dirichlet L-functions with character sums and the related properties of character sums to study the mean value of the general Dedekind sums over interval [1,qp), and give some interesting asymptotic formulae.<\/jats:p>","DOI":"10.3390\/sym12122079","type":"journal-article","created":{"date-parts":[[2020,12,15]],"date-time":"2020-12-15T09:12:57Z","timestamp":1608023577000},"page":"2079","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Mean Value of the General Dedekind Sums over Interval                                                       \\({[1,\\frac{q}{p})}\\)"],"prefix":"10.3390","volume":"12","author":[{"given":"Lei","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics, Northwest University Xi\u2019an, Xi\u2019an 710069, China"}]},{"given":"Zhefeng","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Mathematics, Northwest University Xi\u2019an, Xi\u2019an 710069, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"513","DOI":"10.2140\/pjm.1953.3.513","article-title":"The reciprocity theorem of Dedekind sums","volume":"3","author":"Carlitz","year":"1953","journal-title":"Pac. 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