Hybrid Power Mean of Inversion of L Functions and Gauass Sums

Abstract

newlineMotivated with the development of Hybrid newlinepower mean and asymptotic formula for newlinesome exponential sums and L-function newlineby earlier authors namely Wenpeng newlineZhang, newlineYuping Deng, S. Chowla, newlineLiu Huaning, newlineHan Zhang, Xiaowei Pan, newlineHerbert Walumn newlineetc., newlinewe consider the problem newlineof finding newlinehybrid power mean of Gauss sum and L- newlinefunctions. In this direction we extend the work of newlineZhang and found the asymptotic newlinebehaviour of various newlineexponential sums. Also with the motivation by the work of L. newlineHonyan, L. K. Hua, S. H. Min, H. Yuan, Q. Y. Liao, D. Han, M. Rong, Q. Tian, newlineL. Xiaoxue, Y. Yuan and others, we introduce some new mean values of these newlinehybrid sums and study their asymptotic behaviour. We concentrate our studyto newlinefind hybrid power mean for various type of exponential suns, asynptotic formula. newlineChapter newline1 is the introduction which deals newlinewith the detailed literature survey newlinein the problem of finding hybrid newlinepower newlinemean of Gauss sum newlineand some other newlineexponential sums. newlineChapter 2 newlinecontains the detailed study newlineof general Gauss sum, newlinegeneral quartic Gauss sum, newlinecode and different newlinepower of hybrid newlinemeans. Similarly, newlineaverage and inversion of newlineDirichlet L-functions are also newlinediscussed in detail.