It is a classical result in elliptic function theory that for every elliptic function there is an algebraic addition theorem. In this note we wish to show that such results really depend only on the fact that one is dealing with analytic functions which are finite-to-one in a certain strong sense.
Addition theorems on Zn
β Scribed by Li Fuzhong; Weidong Gao
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 165 KB
- Volume
- 137
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
Let Z. be the cyclic group of order n. For a sequence S of elements in Z., we usef(S) to denote the number of subsequences of S that the sum of whose terms is zero. In this paper, we determine all sequences S of elements in Z. for which ~<f(S)/[Sl-<l
π SIMILAR VOLUMES
Let S=(a 1 , a 2 , ..., a 2n&1 ) be a sequence of 2n&1 elements in an Abelian group G of order n (written additively). For a # G, let r(S, a) be the number of subsequences of length exactly n whose sum is a. Erdo s et al. [1] proved that r(S, 0) 1. In [2], Mann proved that if n (=p) is a prime, then
It is well known that if a,, . , a, are residues module n and m an then some sum ai, + . . .+q,, iI<...<&, is 0 (mod n). In recent related work, Sydney Bulman-Fleming and Edward T.H. Wang have studied what they call n-divisible subsequences of a finite sequence u, and made a number of conjectures. W