On the 2kth power mean of the character sums over short intervals

A note on the $2k$-th power mean of character sums over the quarter interval

“…From our theorem and the theorem in [6], we find that odd and even primitive characters have a very different contribution to the higher moment of character sums over the quarter interval. For the case k = 2, from Corollaries 1.2 and 1.3, we see that the contribution of odd primitive characters is six times that of the even ones, although (see Remark 2.4 in the next section)…”

“…In this paper we study odd primitive character sums over the interval [1, q 4 ) by transforming them to L-functions, and we obtain an asymptotic formula for the 2k-th power mean using the same method as in [6]. …”

“…Burgess [5] denotes the sum over all primitive characters modulo q and τ (n) is the divisor function. The author and Zhang [6] studied the 2k-th power mean of the even primitive character sums over the quarter interval [1, denotes the sum over all primitive characters modulo q such that χ(−1) = 1, is any fixed positive number, J(q) denotes the number of all primitive characters modulo q, p|q denotes the product over all prime divisors p of q, and…”

On a kind of generalized Lehmer problem

“…There are many other results about the problem by a lot of scholars ( [6], [5], [3], [4]). Let E 1 , E 2 , .…”

Fourth power mean of character sums

“…In order to obtain an asymptotic formula for higher moments of character sums, the authors [7] studied the 2kth power mean of the even primitive character sums over the quarter interval [ …”