theta function वाक्य

उदाहरण वाक्य

1. The importance of this concept was realised first in the analytic theory of theta functions, and geometrically in the theory of bitangents.
2. However, application of this formula in practice is difficult because the relevant hyperelliptic integrals and higher genus theta functions are very complex.
3. Hecke found generalised characters of number fields, now called Hecke characters, for which his proof ( based on theta functions ) also worked.
4. a ratio of Jacobi theta functions \ theta _ { m }, and is the square of the elliptic modulus k ( \ tau ).
5. Zwegers's fundamental result shows that mock theta functions are the " holomorphic parts " of real analytic modular forms of weight 1 / 2.
6. Later in his career, Coble also studied the relations between hyperelliptic theta functions, irrational binary invariants, the Weddle surface and the Kummer surface.
7. His research was on differential geometry ( especially geodesics on " n "-dimensional manifolds ), Riemann surfaces, and theta functions.
8. If is fixed, this becomes a Fourier series for a periodic entire function of with period 1; in this case, the theta function satisfies the identity
9. When integrating over surfaces such as the torus, we end up with equations in terms of theta functions and elliptic functions such as the Dedekind eta function.
10. General solutions of the spatially periodic initial value problem for the heat equation may be obtained by convolving the initial data at 0 } } with the theta function.