EuDML | Browse

Items

All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Displaying 2301 – 2320 of 3014

On the mean value of the mixed exponential sums with Dirichlet characters and general Gauss sum

Yongguang Du, Huaning Liu (2013)

Czechoslovak Mathematical Journal

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 $χ$ , $\bar{χ}$ modulo $q$ we define a mixed exponential sum $C (m, n; k; χ; \bar{χ}; q) = \sum_{a = 1}^{q} {w i d t h 0 p t h e i g h t 1 e m}^{'} χ (a) G_{k} (a, \bar{χ}) e (\frac{m a^{k} + n \bar{a^{k}}}{q}),$ with Dirichlet character $χ$ and general Gauss sum $G_{k} (a, \bar{χ})$ as coefficient, where $\sum^{'}$ denotes the summation over all $a$ such that $(a, q) = 1$ , $a \bar{a} \equiv 1 mod q$ and $e (y) = e^{2 π i y}$ . We mean value of $\sum_{m} \sum_{χ} \sum_{\bar{χ}} {| C (m, n; k; χ; \bar{χ}; q) |}^{4},$ and...

In this paper we study the asymptotic behavior of the mean value of Dedekind sums, and give a sharper asymptotic formula.

Currently displaying 2301 – 2320 of 3014

Previous Page 116 Next

Displaying 2301 – 2320 of 3014

On the mean value of the mixed exponential sums with Dirichlet characters and general Gauss sum

On the mean value of the remainder term of the prime number formula

On the mean values and distributions of arithmetic functions

On the mean values of Dedekind sums

On the measure of measurable sets of integers

On the meromorphic continuation of degree two $L$ -functions.

On the method of Coleman and Chabauty.

On the method of exponent pairs

On the metric theory of continued fractions

On the metric theory of continued fractions

On the metric theory of inhomogeneous diophantine approximations

On the Metric Theory of the Nearest Integer Continued Fraction expansion.

On the Milnor exact sequence for global function fields

On the Milnor $K$ -groups of complete discrete valuation fields.

On the minimum of the unit lattice

On the Möbius function.

On the Möbius sum function

On the moderate growth of generalized Dirichlet series for hypoelliptic polynomials

On the modular curve $X_{E} (7)$ . (Sur la courbe modulaire $X_{E} (7)$ .)

On the modular curve $X_{ndép} (11)$ . (Sur la courbe modulaire $X_{ndép} (11)$ .)

Currently displaying 2301 – 2320 of 3014