The study of the power mean of the generalized polynomial exponential sums plays a very important role in analytic number theory, and many classical number theory problems are closely related to it. In this article, we use the elementary methods and the properties of the exponential sums to study the calculating problem of one kind of fourth power mean of some special generalized polynomial exponential sums, and we give some exact calculating formulae for them.
Citation: Li Wang, Yuanyuan Meng. Generalized polynomial exponential sums and their fourth power mean[J]. Electronic Research Archive, 2023, 31(7): 4313-4323. doi: 10.3934/era.2023220
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The study of the power mean of the generalized polynomial exponential sums plays a very important role in analytic number theory, and many classical number theory problems are closely related to it. In this article, we use the elementary methods and the properties of the exponential sums to study the calculating problem of one kind of fourth power mean of some special generalized polynomial exponential sums, and we give some exact calculating formulae for them.
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Li Wang, Yuanyuan Meng. Generalized polynomial exponential sums and their fourth power mean[J]. Electronic Research Archive, 2023, 31(7): 4313-4323. doi: 10.3934/era.2023220
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