A function or a power series f is called differentially algebraic if it satisfies a Ε½ X Ε½ n. . differential equation of the form P x, y, y , . . . , y s 0, where P is a nontrivial polynomial. This notion is usually defined only over fields of characteristic zero and is not so significant over fields
Some transcendental functions over function fields with positive characteristic
β Scribed by Jia-Yan Yao
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 66 KB
- Volume
- 334
- Category
- Article
- ISSN
- 1631-073X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We apply the S-unit theorem for a function field K with positive characteristic to show that under certain conditions the height of the S-integral points of P n (K)&[2n+2 hyperplanes in general position] is bounded. We also provide examples to show that the conditions are necessary. 1999 Academic P
Using Drinfeld modular curves we determine the places of supersingular reduction of elliptic curves over F 2 r( T) with certain conductors. This enables us to classify and describe explicitly all elliptic curves over F 2 r( T ) having a conductor of degree 4. Our results also imply that extremal ell
It is shown that, for every integer n >t 2, there exist distribution functions F on the real line (which may be chosen to be of lattice type or absolutely continuous) such that (i) F has moments of all orders, and (ii) the convolutions F\*', 1 ~< r ~< n -1, ofF with itself are all asymmetric about t
We investigate theta functions attached to quadratic forms over a number field K. We establish a functional equation by regarding the theta functions as specializations of symplectic theta functions. By applying a differential operator to the functional equation, we show how theta functions with har