Examples of finite p-divisible sets of MHS
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چکیده
The following examples give evidence to the following conjecture contained in my paper [2]. All the main theoretical results can be found in that paper. Conjecture 1. Let d be a positive integer and ~s ∈ N. Then the set J(~s|p) is finite for every prime p. Example 2. The first example we would like to do is about the partial sums of ζ(2) series. The prime p = 7 is a little different from the others because H(2; 3) = 49/36. We find that
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ar X iv : 0 80 6 . 49 47 v 1 [ m at h . N T ] 3 0 Ju n 20 08 Examples of finite p - divisible sets of MHS
The following examples give evidence to the following conjecture contained in my paper [2]. All the main theoretical results can be found in that paper. Conjecture 1. Let d be a positive integer and ~s ∈ N. Then the set J(~s|p) is finite for every prime p. Example 2. The first example we would like to do is about the partial sums of ζ(2) series. The prime p = 7 is a little different from the ot...
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Hence J2(2|7) = ∅ and consequently J(2|7) = {0, 3, 6, 26}. For all the other primes p 6= 7 from 5 up to 1061 we find that J1(2|p) = {0, (p− 1)/2, p− 1} ∪ T (2|p) ∪ {p− 1− r : r ∈ T (2|p)} where T (2|p) are listed in Table 1 if T (2|p) 6= ∅. Moreover, J1(2|p) = ∅ which implies J(2|p) = {(p− 1)/2, p− 1} ∪ T (2|p) ∪ {p− 1− r : r ∈ T (2|p)} in this range. p T (2|p) p T (2|p) p T (2|p) p T (2|p) p T...
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