Results 1 to 10 of about 7,405,970 (315)

A Conversion Formula for One Kind Fourth Power Mean of Kloosterman Sums and the Character Sums Module p

Journal of Mathematics
The primary contribution of this paper is to research one kind special Kloosterman sums using analytic method. We translate one kind fourth power mean of the Kloosterman sums into the character sums of one kind polynomials. It is possible to construct an
Shushu Ning, Xuexia Wang
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On an exponential D. H. Lehmer problem

Electronic Research Archive
For an odd prime $ p $ and a positive integer $ \alpha $, let $ g $ be of multiplicative order $ \tau $ modulo $ q $ and $ q = p^{\alpha} $. Denote by $ N(h, g, q) $ the number of $ a $ such that $ h\nmid (a+(g^{a})_{q}) $ for any $ 1\leq a\leq \tau ...
Zhefeng Xu, Jiankang Wang , Lirong Zhu
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Application of spectral theory to number theory [PDF]

Rocky Mountain Journal of Mathematics, 1985
An introductory non-technical survey is given of relations between real analytic modular forms on the upper half plane and questions in number theory. Recommended.
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Hybrid mean value involving some two-term exponential sums and fourth Gauss sums

Electronic Research Archive
Let $ q\ge3 $ be a positive integer. For any integers $ m $, $ n $, $ k $, $ h $, the two-term exponential sums $ C(m, n, k, h; q) $ is defined as $ C(m, n, k, h;q) = \sum\limits_{a = 1}^{q}e\left(\frac{ma^k+na^h}{q}\right) $, where $ k > h\ge 2 $.
Zhefeng Xu, Xiaoying Liu, Luyao Chen
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New family of special numbers associated with finite operator [PDF]

Mathematica Moravica, 2020
Using the notion of the generating function of a function, we define an operator with whom we manage to build a large family of numbers and polynomials. This technique permits to give the closed formulae and interesting combinatorial identities.
Goubi Mouloud
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String theories and prime number theories [PDF]

Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1986
The article consists of two at the moment rather disjoint parts. The first part consists of a simple remark that certain results from the moduli space approach to string theory (Polyakov strings) can be combined to give results in arithmetic algebraic geometry.
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New Proof of the Property of Stirling Number Based on Fubini Polynomials

Journal of Mathematics
The main purpose of this article is using the elementary methods and the properties of the Fubini polynomials to study the congruence properties of a signless Stirling number of the first kind and solve a conjecture proposed by J. H. Zhao and Z. Y. Chen.
Li Wang, Xiaoge Liu
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The height of q-Binary Search Trees [PDF]

Discrete Mathematics & Theoretical Computer Science, 2002
q-binary search trees are obtained from words, equipped with a geometric distribution instead of permutations. The average and variance of the heighth computated, based on random words of length n, as well as a Gaussian limit law.
Michael Drmota, Helmut Prodinger
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Theorem of the complex exponentials

Ratio Mathematica, 2019
This paper describes a new theorem that relates the lengths of the legs of a right triangle with the ratio of three complex exponentials. The big novelty of the theorem consists in transforming two real measures of legs derived from Euclidean geometry ...
Alberto Daunisi
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The distribution of ascents of size d or more in compositions [PDF]

Discrete Mathematics & Theoretical Computer Science, 2009
Combinatorics
Charlotte Brennan, Arnold Knopfmacher
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