Fine Addition Theorems, II
β Scribed by A. Sarkozy
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 547 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0022-314X
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π SIMILAR VOLUMES
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.
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
We establish several addition theorems on finite abelian groups by employing a group ring as a useful tool. Among several results the following is proved. Let p be a prime, and let G=Z p e 1 } } } Z p e n with 1 e 1 } } } e n . Put w=(1Γ( p en &1)) \_ n i=1 ( p e i &1). Then, for any t ( p en &1) lo