We give an explicit p-adic expansion of np j=1, ( j, p)=1 j &r as a power series in n. The coefficients are values of p-adic L-functions. 1998 Academic Press Several authors (see [2, pp. 95 103]) have studied the sums : np j=1 ( j, p)=1 k=1 \ &r k + L p (r+k, | 1&k&r )( pn) k
Canonical Curves and Varieties of Sums of Powers of Cubic Polynomials
β Scribed by Atanas Iliev; Kristian Ranestad
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 110 KB
- Volume
- 246
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
β¦ Synopsis
In this note we show that the apolar cubic forms associated to codimension 2 linear sections of canonical curves of genus g β₯ 11 are special with respect to their presentation as sums of cubes.
π SIMILAR VOLUMES
We determine the HilbertαKunz function of plane elliptic curves in odd characteristic, as well as over arbitrary fields the generalized HilbertαKunz functions of nodal cubic curves. Together with results of K. Pardue and P. Monsky, this completes the list of HilbertαKunz functions of plane cubics. C
As an extension of the Linnik Gallagher results on the ``almost Goldbach'' problem, we prove that every large even integer is a sum of four squares of primes and 8330 powers of 2.
We present a simple and general algebraic technique for obtaining results in Additive Number Theory, and apply it to derive various new extensions of the Cauchy Davenport Theorem. In particular we obtain, for subsets A 0 , A 1 , ..., A k of the finite field Z p , a tight lower bound on the minimum p
In the "rst part of the paper, certain incomplete character sums over a "nite "eld F N P are considered which in the case of "nite prime "elds F N are of the form , where A and N are integers with 14N(p, g and f are polynomials over F N , and denotes a multiplicative and an additive character of F