Related papers: Robba's method on exponential sums
Sharp quadrature formulas for integrals of complex rational functions on circles, real axis and its segments are obtained. We also find sharp quadrature formulas for calculation of $L_2$-norms of rational functions on such sets. Basing on…
Let $f(n)$ be an arithmetic function with $f(n) \ll n^\alpha$ for some $\alpha\in[0,1)$ and let $\lfloor .\rfloor $ denote the integer part function. In this paper, we evaluate asymptotically the sums $$\sum_{n_{1}n_{2}\leq x}f \left(…
I am going to provide a new technique of approximating area under the curve, using the Newton-Raphson Method. I am also going to provide a formula that would help us approximate any Definite Integral or help us find the area under the…
Using classical results of Rogers bounding the $L^2$-norm of Siegel transforms, we give bounds on the heights of approximate integral solutions of quadratic equations and error terms in the quantiative Oppenheim theorem of…
We have shown that a Lagrangian for a torus surface can yield second order nonlinear differential equations using the Euler-Lagrange formulation. It is seen that these second order nonlinear differential equations can be transformed into…
We obtain an asymptotic formula for the L^1 norm of the exponential sum $M(\alpha) = \sum_{n\le X}\tau(n)e(n\alpha)$ where $\tau(n) = \sum_{d|n} 1$ is the divisor function. In particular, we show that it is $\sim C\sqrt{X}\log X$ with $C =…
In this paper, we propose a new method that combines the inexact Newton method with a procedure to obtain a feasible inexact projection for solving constrained smooth and nonsmooth equations. The local convergence theorems are established…
To investigate the topological structure of Morse functions on the projective plane we use the Reeb graphs. We describe it properties and prove that it is a complete topological invariant of simple Morse function on $\mathbb{R} P^2$. We…
We present a simple yet powerful technique for forming iterative methods of various convergence orders. Methods of various convergence orders (four, six, eight and ten) are formed through a modest modification of the classical Newton…
In the first paper of this series we established new upper bounds for multi-variable exponential sums associated with a quadratic form. The present study shows that if one adds a linear term in the exponent, the estimates can be further…
In a former paper it has been shown that the elliptic Gau{\ss} sums, whose use has been proposed in the context of counting points on elliptic curves and primality tests, can be computed by using modular functions. In this work we give…
In this paper, we use methods of exponential sums to derive a formula for estimating effective upper bounds of $|\zeta'(1/2+it)|$. Different effective upper bounds can be obtained by choosing different parameters.
We introduce a "resonance" method to produce large values of $|\zeta(1/2+it)|$ and large and small central values of $L$-functions.
In this paper, the formulas of some exponential sums over finite field, related to the Coulter's polynomial, are settled based on the Coulter's theorems on Weil sums, which may have potential application in the construction of linear codes…
``Quasi-elliptic'' functions can be given a ring structure in two different ways, using either ordinary multiplication, or convolution. The map between the corresponding standard bases is calculated. A related structure has appeared…
The use of trigonometric polynomials as Lagrange multipliers in the harmonic mortar method enables an efficient and elegant treatment of relative motion in the stator-rotor coupling of electric machine simulation. Explicit formulas for the…
Starting from a classical generating series for Bessel functions due to Schlomilch, we use Dwork's relative dual theory to broadly generalize unit-root results of Dwork on Kloosterman sums and Sperber on hyperkloosterman sums. In…
Borell's formula is a stochastic variational formula for the log-Laplace transform of a function of a Gaussian vector. We establish an extension of this to the Riemannian setting and give a couple of applications, including a new proof of a…
In this work the authors use their contour integral method to derive a double integral connected to the modified Bessel function of the second kind and express it in terms of the Lerch function. There are some useful results relating double…
We develop the first stochastic incremental method for calculating the Moore-Penrose pseudoinverse of a real matrix. By leveraging three alternative characterizations of pseudoinverse matrices, we design three methods for calculating the…