The various properties of classical Dedekind sums $S(h, q)$ have been investigated by many authors. For example, Yanni Liu and Wenpeng Zhang: A hybrid mean value related to the Dedekind sums and Kloosterman sums, Acta Mathematica Sinica, 27 (2011), 435–440 studied the hybrid mean value properties involving Dedekind sums and generalized Kloosterman sums $K(m, n, r; q)$. The main purpose of this paper, is using the analytic methods and the properties of character sums, to study the computational problem of one kind of hybrid mean value involving Dedekind sums and generalized Kloosterman sums, and give an interesting identity.
This paper proposes a non-trivial definition of the notion of analytic method. Working within the so-called instructional model of method, I distinguish three kinds of instructions which occur in methods: selective, executive, and declarative instructions. I discuss the relation between each of these and the analyticity of a method. Then I define the notions of an analytic use of an instruction and of an analytic instruction, which are at the basis of the proposed definition of an analytic method. Finally, I discuss the issue of circularity in the presented model which arises if we consider a finite agent testing a method for analyticity., Tato práce navrhuje netriviální definici pojmu analytická metoda. V rámci tzv. Instruktážního modelu metody rozlišuji tři druhy instrukcí, které se vyskytují v metodách: selektivní, exekutivní a deklarativní . Diskutuji o vztahu mezi každou z nich a analytičnosti metody. Dále definuji pojmy analytického použití instrukce a analytické instrukce , které jsou základem navrhované definice analytické metody. Závěrem se zabývám otázkou kruhovitosti v prezentovaném modelu, která vzniká, pokud uvažujeme konečný agent testující metodu analyticity., and Miloš Kosterec
For any positive integer k ≥ 3, it is easy to prove that the k-polygonal numbers are an(k) = (2n+n(n−1)(k−2))/2. The main purpose of this paper is, using the properties of Gauss sums and Dedekind sums, the mean square value theorem of Dirichlet L-functions and the analytic methods, to study the computational problem of one kind mean value of Dedekind sums S(an(k)ām(k), p) for k-polygonal numbers with 1 ≤ m, n ≤ p − 1, and give an interesting computational formula for it., Jing Guo, Xiaoxue Li., and Obsahuje seznam literatury
About Lehmer’s number, many people have studied its various properties, and obtained a series of interesting results. In this paper, we consider a generalized Lehmer problem: Let p be a prime, and let N(k; p) denote the number of all 1\leqslant a_{i}\leq p-1 such that a_{1}a_{2}...a_{k}\equiv 1 mod p and 2 | ai + āi + 1, i = 1, 2, ..., k. The main purpose of this paper is using the analytic method, the estimate for character sums and trigonometric sums to study the asymptotic properties of the counting function N(k; p), and give an interesting asymptotic formula for it., Han Zhang, Wenpeng Zhang., and Obsahuje seznam literatury