Results 11 to 20 of about 37 (37)
Rational points on complete intersections over Fq(t)${\mathbb {F}}_q(t)$
Proceedings of the London Mathematical Society, Volume 126, Issue 2, Page 556-619, February 2023., 2023 Abstract A 2‐dimensional version of Farey dissection for function fields K=Fq(t)$K=\mathbb {F}_q(t)$ is developed and used to establish the quantitative arithmetic of the set of rational points on a smooth complete intersection of two quadrics X⊂PKn−1$X\subset \mathbb {P}^{n-1}_{K}$, under the assumption that q$q$ is odd and n⩾9$n\geqslant 9$.
Pankaj Vishe
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On the Hybrid Power Mean Involving the Character Sums and Dedekind Sums
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 The main purpose of this paper is to use the elementary and analytic methods, the properties of Gauss sums, and character sums to study the computational problem of a certain hybrid power mean involving the Dedekind sums and a character sum analogous to Kloosterman sum and give two interesting identities for them.
Xiaoling Xu, Yuan Yi
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A Hybrid Mean Value Involving Dedekind Sums and the Generalized Kloosterman Sums
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 In this paper, we use the mean value theorem of Dirichlet L‐functions and the properties of Gauss sums and Dedekind sums to study the hybrid mean value problem involving Dedekind sums and the general Kloosterman sums and give an interesting identity for it.
Xiaowei Pan, Xiaoyan Guo, Tianping Zhang
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Software for Genome‐Wide Association Studies in Autopolyploids and Its Application to Potato
The Plant Genome, Volume 9, Issue 2, July 2016., 2016 Genome‐wide association studies (GWAS) are widely used in diploid species to study complex traits in diversity and breeding populations, but GWAS software tailored to autopolyploids is lacking. The objectives of this research were to (i) develop an R package for autopolyploids based on the Q + K mixed model, (ii) validate the software with simulated ...
Umesh R. Rosyara +3 more
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A New Sum Analogous to Gauss Sums and Its Fourth Power Mean
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate for it.
Shaofeng Ru +2 more
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New Mixed Exponential Sums and Their Application
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 The main purpose of this paper is to introduce a new mixed exponential sums and then use the analytic methods and the properties of Gauss sums to study the computational problems of the mean value involving these sums and give an interesting computational formula and a sharp upper bound estimate for these mixed exponential sums.
Yu Zhan, Xiaoxue Li, Ashraf Zenkour
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On the Generalization of Lehmer Problem and High‐Dimension Kloosterman Sums
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 For any fixed integer k ≥ 2 and integer r with (r, p) = 1, it is clear that there exist k integers 1 ≤ ai ≤ p − 1 (i = 1, 2, … , k) such that a1a2 ⋯ ak ≡ r mod p. Let N(k, r; p) denote the number of all (a1, a2, ⋯ ak) such that a1a2 ⋯ ak ≡ r mod p and 2†(a1 + a2 + ⋯ + ak).
Guohui Chen, Han Zhang, Kinkar Ch Das
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A Hybrid Mean Value Involving Dedekind Sums and the General Exponential Sums
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 The main purpose of this paper is using the analytic method, A. Weil’s classical work for the upper bound estimate of the general exponential sums, and the properties of Gauss sums to study the hybrid mean value problem involving Dedekind sums and the general exponential sums and give a sharp asymptotic formula for it.
Jianghua Li, Tingting Wang, Reza Ansari
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On a Kind of Dirichlet Character Sums
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 Let p ≥ 3 be a prime and let χ denote the Dirichlet character modulo p. For any prime q with q < p, define the set Eq,p=a∣11≤a,a-≤p,aa-≡modp and a≡a-modq. In this paper, we study a kind of mean value of Dirichlet character sums ∑a≤p a∈Eq,p χ(a), and use the properties of the Dirichlet L‐functions and generalized Kloosterman sums to obtain an ...
Rong Ma +3 more
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Fourier expansions of complex‐valued Eisenstein series on finite upper half planes
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 We consider complex‐valued modular forms on finite upper half planes Hq and obtain Fourier expansions of Eisenstein series invariant under the groups Γ=SL(2,Fp) and GL(2,Fp). The expansions are analogous to those of Maass wave forms on the ordinary Poincaré upper half plane —the K‐Bessel functions being replaced by Kloosterman sums.
Anthony Shaheen, Audrey Terras
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