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2. A Nevanlinna theorem for superharmonic functions on Dirichlet regular Greenian sets
- Creator:
- Watson, Neil A.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Nevanlinna theorem, superharmonic function, δ-subharmonic function, Riesz measure, and mean value
- Language:
- English
- Description:
- A generalization of Nevanlinna’s First Fundamental Theorem to superharmonic functions on Green balls is proved. This enables us to generalize many other theorems, on the behaviour of mean values of superharmonic functions over Green spheres, on the Hausdorff measures of certain sets, on the Riesz measures of superharmonic functions, and on differences of positive superharmonic functions.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
3. A note on the mean value of the general Kloosterman sums
- Creator:
- Yao, Weili
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- the general Kloosterman sums, mean value, and calculating formula
- Language:
- English
- Description:
- The main purpose of this paper is to use the analytic method to study the calculating problem of the general Kloosterman sums, and give an exact calculating formula for it.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
4. Mean value theorems for divided differences and approximate Peano derivatives
- Creator:
- Mukhopadhyay, S. N. and Ray, S.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- mean value, higher order divided difference, approximate Peano derivative, and n-convex function
- Language:
- English
- Description:
- Several mean value theorems for higher order divided differences and approximate Peano derivatives are proved.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
5. On the k-polygonal numbers and the mean value of Dedekind sums
- Creator:
- Guo, Jing and Li, Xiaoxue
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, hodnoty, Dedekindovy okruhy, mathematics, values, Dedekind rings, Dedekind sums, mean value, computational problem, k-polygonal number, analytic method, 13, and 51
- Language:
- English
- Description:
- 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
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
6. On the mean value of Dedekind sum weighted by the quadratic Gauss sum
- Creator:
- Wang, Tingting and Zhang, Wenpeng
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Dedekind sum, quadratic Gauss sum, mean value, and identity
- Language:
- English
- Description:
- Various properties of classical Dedekind sums $S(h, q)$ have been investigated by many authors. For example, Wenpeng Zhang, On the mean values of Dedekind sums, J. Théor. Nombres Bordx, 8 (1996), 429–442, studied the asymptotic behavior of the mean value of Dedekind sums, and H. Rademacher and E. Grosswald, Dedekind Sums, The Carus Mathematical Monographs No. 16, The Mathematical Association of America, Washington, D.C., 1972, studied the related properties. In this paper, we use the algebraic method to study the computational problem of one kind of mean value involving the classical Dedekind sum and the quadratic Gauss sum, and give several exact computational formulae for it.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
7. On the mean value of the mixed exponential sums with Dirichlet characters and general Gauss sum
- Creator:
- Du, Yongguang and Liu, Huaning
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- mixed exponential sum, mean value, Dirichlet character, general Gauss sum, and computational formula
- Language:
- English
- Description:
- The main purpose of the paper is to study, using the analytic method and the property of the Ramanujan's sum, the computational problem of the mean value of the mixed exponential sums with Dirichlet characters and general Gauss sum. For integers $m$, $ n$, $ k$, $ q$, with $k\geq {1}$ and $q\geq {3}$, and Dirichlet characters $\chi $, $\bar {\chi }$ modulo $q$ we define a mixed exponential sum $$ C(m,n;k;\chi ;\bar {\chi };q)= \sum \limits _{a=1}^{q}{\mkern -4mu\vrule width0pt height1em}' \chi (a)G_{k}(a,\bar {\chi })e \Big (\frac {ma^{k}+n\overline {a^{k}}}{q}\Big ), $$ with Dirichlet character $\chi $ and general Gauss sum $G_{k}(a,\bar {\chi })$ as coefficient, where $\sum \nolimits '$ denotes the summation over all $a$ such that $(a,q)=1$, $a\bar {a}\equiv {1}\mod {q}$ and $e(y)={\rm e}^{2\pi {\rm i} y}$. We mean value of $$ \sum _{m}\sum _{\chi }\sum _{\bar {\chi }}|C(m,n;k;\chi ;\bar {\chi };q)|^{4}, $$ and give an exact computational formula for it.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public