Sentence examples for a very elementary way from inspiring English sources

Mordell [19] see also [20] proved the functional relation for ζ ( s, a ) in (1.10) and that ζ ( s, a ) can be continued meromorphically to the whole s plane except for a simple pole at s = 1, in a very elementary way, by using Poisson's summation formula.

In this paper, firstly, we show that by using the Poisson summation formula, the analytic continuation of the Lerch zeta function can be explained and the functional relation for the Lerch zeta function can be obtained in a very elementary way.

The present proof is very direct, and relies instead on introducing a family of equivalent weighted norms indexed by a parameter $\beta$ and to make an appropriate choice of this parameter that allows to combine in a very elementary way the two ingredients (existence of a Lyapunov function and irreducibility) that are crucial in obtaining a spectral gap.

"Don't You Know I Love You" is a very elementary song.

Mr. Brosnan added: "At a very elementary level it is a partnership between two iconic American brands".

A very elementary example concerns the exponent notation.

As a very elementary illustration, suppose one seeks a (bar{partial }) estimate in ordinary (L^2) norms, i.e., (phi =0).

The two last integrals can be computed in an elementary way.

We prove in an elementary way that if,,, the above nonlinear integral equation has no positive solution.

A very long way, indeed.

In a very subtle way".