Results 11 to 20 of about 146 (139)
Generalization of the Lehmer problem over incomplete intervals
Journal of Inequalities and Applications, 2023 Let α ≥ 2 $\alpha \geq 2$ , m ≥ 2 $m\geq 2 $ be integers, p be an odd prime with p ∤ m ( m + 1 ) $p\nmid m (m+1 )$ , 0 < λ 1 $0 max { [ 1 λ 1 ] , [ 1 λ 2 ] } $q=p^{\alpha }> \max \{ [ \frac{1}{\lambda _{1}} ], [ \frac{1}{\lambda _{2}} ] \}$ .
Zhaoying Liu, Di Han
doaj +1 more source
Double sums of Kloosterman sums in finite fields [PDF]
Finite Fields and Their Applications, 2019 We bound double sums of Kloosterman sums over a finite field ${\mathbb F}_{q}$, with one or both parameters ranging over an affine space over its prime subfield ${\mathbb F}_p \subseteq {\mathbb F}_{q} $. These are finite fields analogues of a series of recent results by various authors in finite fields and residue rings.
Simon Macourt, Igor E. Shparlinski
openaire +2 more sources
On the Hybrid Mean Value Involving Kloosterman Sums and Sums Analogous to Dedekind Sums
Abstract and Applied Analysis, 2013 The main purpose of this paper is using the properties of Gauss sums and the mean value theorem of Dirichlet L-functions to study one kind of hybrid mean value problems involving Kloosterman sums and sums analogous to Dedekind sums and give two exact ...
Di Han, Wenpeng Zhang
doaj +1 more source
On general partial Gaussian sums
Journal of Inequalities and Applications, 2016 Let q ≥ 2 $q\geq2$ be a fixed integer, A = A ( q ) ≤ q $A=A(q)\leq q$ , B = B ( q ) ≤ q $B=B(q)\leq q$ , and H = H ( q ) ≤ q $H=H(q)\leq q$ . Define ħ ( A , B , H ) = { a ∈ Z ∣ ( a , q ) = 1 , a b ≡ 1 ( mod q ) , 1 ≤ a ≤ A , 1 ≤ b ≤ B , | a − b | ≤ H } .
Ganglian Ren +2 more
doaj +1 more source
On the first power mean of L-functions with the weight of general Kloosterman sums
International Journal of Mathematics and Mathematical Sciences, 2002 The main purpose of this paper is using the estimates for character sums and the analytic method to study the first power mean of Dirichlet L-functions with the weight of general Kloosterman sums, and give an interesting asymptotic formula.
Zhang Wenpeng
doaj +1 more source
Character sums over generalized Lehmer numbers
Journal of Inequalities and Applications, 2016 Let q > 2 $q>2$ be an integer, n ⩾ 2 $n\geqslant2$ be a fixed integer with ( n , q ) = 1 $(n,q)=1$ , ψ be a non-principal Dirichlet character modq. An upper bound estimate for character sums of the form ∑ a ∈ C ( 1 , q ) ψ ( a ) $$\sum_{a\in\textit{C}(1 ...
Yuankui Ma +3 more
doaj +1 more source
Cancellations amongst Kloosterman sums [PDF]
Acta Arithmetica, 2016 We obtain several estimates for bilinear form with Kloosterman sums. Such results can be interpreted as a measure of cancellations amongst with parameters from short intervals. In particular, for certain ranges of parameters we improve some recent results of Blomer, Fouvry, Kowalski, Michel, and Milićević (2014) and Fouvry, Kowalski and Michel (2014).
Shparlinski, Igor E., Zhang, Tianping
openaire +2 more sources
On a Kind of Dirichlet Character Sums
Abstract and Applied Analysis, 2013 Let p≥3 be a prime and let χ denote the Dirichlet character modulo p.
Rong Ma, Yulong Zhang, Guohe Zhang
doaj +1 more source
Kloosterman sums with multiplicative coefficients [PDF]
Science China Mathematics, 2015 Let $f(n)$ be a multiplicative function satisfying $|f(n)|\leq 1$, $q$ $(\leq N^2)$ be a positive integer and $a$ be an integer with $(a,\,q)=1$. In this paper, we shall prove that $$\sum_{\substack{n\leq N\\ (n,\,q)=1}}f(n)e({a\bar{n}\over q})\ll\sqrt{τ(q)\over q}N\log\log(6N)+q^{{1\over 4}+{ε\over 2}}N^{1\over 2}(\log(6N))^{1\over 2}+{N\over \sqrt ...
Gong, Ke, Jia, Chaohua
openaire +2 more sources
Fourier expansions of complex-valued Eisenstein series on finite upper half planes
International Journal of Mathematics and Mathematical Sciences, 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).
Anthony Shaheen, Audrey Terras
doaj +1 more source