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I’M SORRY (information is out-of-date… I’m now updating it slowly).

2015

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[11 Oct 2015 | One Comment | 26 views]

Motivated by the (renormalization) of some classical divergent series in String Theory, e.g.

 \sum_{n=1}^{+\infty} n = -\frac{1}{12} \:\:\mbox{ (yes, it means) } 1 + 2+ 3+ 4+5+6+\dots = -\frac{1}{12}

(see here), I start thinking on the convergence meaning of a class of divergent series, trying to make sense of them without following some of the (standard) approaches as Hardy resummation or Zeta function regularization (e.g. wikipedia). The main idea was to see if it is possible to define a class of sequences and a equivalence operation, by aggregating terms, such that their “value” is determined by some constant sequence in the same equivalent class.

In the comments of this post, you see the precise notions and a preliminary result, which is quite open for discussion…