Cancellation in algebraic twisted sums on GL_ m

Let π be an automorphic irreducible cuspidal representation of GL m {\operatorname{GL}_{m}} over ℚ {\mathbb{Q}} with unitary central character, and let λ π ⁢ ( n ) {\lambda_{\pi}(n)} be its n-th Dirichlet series coefficient. We study short sums of isotypic trace functions associated to some sheaves modulo primes q of bounded conductor, twisted by multiplicative functions λ π ⁢ ( n ) {\lambda_{\pi}(n)} and μ ⁢ ( n ) ⁢ λ π ⁢ ( n ) {\mu(n)\lambda_{\pi}(n)} . We are able to establish non-trivial bounds for these algebraic twisted sums with intervals of length of at least q 1 / 2 + ε {q^{1/2+\varepsilon}} for an arbitrary fixed ε > 0 {\varepsilon>0} .

Uniform Convergence of Cosine Series With Coefficient from New Class of General Monotone

General monotone sequences class (GMS) has been introduced by Tikhonov. Then Bogdan Szal extended this class to the new class called new class of general monotone. By using non-negative sequence is called 𝛽 to controle the difference of sine series coefficient. By substituting 𝛽 of modulus of sine series coefficient, we study uniform convergence of new class of general monotone on cosine series.

The Calculation and Estimate of Interval-Valued and Fuzzy Dirichlet Series Coefficient

This article gives the definition of interval-valued Dirichlet series. Based on [1, , this article discusses some properties about the coefficient of interval-valued and fuzzy Dirichlet series. Ihe calculation of coefficient , of interval-valued Dirichlet series and the coefficient of fuzzy Dirichelt series are also discussed. Moreover, some relative theorems and properties are presented.

On recursive stopping of decimation of discrete-time bandlimited signals

For each non-decimated as well as decimated realization discrete-time Fourier series coefficient values, located at Nyquist frequency are calculated, using original speedy recursive expressions based on reverse order processing of the given realizations. The criterion for stopping of multifold decimation of discrete-time bandlimited signals has been developed. The simulation results for the bandlimited signal with a triangularshaped spectrum are presented.