R-sequence, class of blue sequences and Mobius

Paper: R-sequence, a class of blue sequences and non-square numbers (draft)

This is still a draft, ie. any hints, analysis, leak disclosures highly welcome.

One quotation, from Gauss, about Sophie Germain:

But how to describe to you my admiration and astonishment at seeing my esteemed correspondent Monsieur Le Blanc metamorphose himself into this illustrious personage who gives such a brilliant example of what I would find it difficult to believe.

A taste for the abstract sciences in general and above all the mysteries of numbers is excessively rare: one is not astonished at it: the enchanting charms of this sublime science reveal only to those who have the courage to go deeply into it.

But when a person of the sex which, according to our customs and prejudices, must encounter infinitely more difficulties than men to familiarize herself with these thorny researches, succeeds nevertheless in surmounting these obstacles and penetrating the most obscure parts of them, then without doubt she must have the noblest courage, quite extraordinary talents and superior genius.

Indeed nothing could prove to me in so flattering and less equivocal manner that the attractions of this science, which has enriched my life with so many joys, are not chimerical, the predilection with which you have honored it.

Kronecker added:

… the introduction of various concepts by the help of which it has frequently been attempted in recent times (but first by Heine) to conceive and establish the “irrationals” in general. Even the concept of an infinite series, for example one which increases according to definite powers of variables, is in my opinion only permissible with the reservation that in every special case, on the basis of the arithmetic laws of constructing terms (or coefficients), … certain assumptions must be shown to hold which are applicable to the series like finite expressions, and which thus make the extension beyond the concept of a finite series really unnecessary.


About misha

Imagine a story that one can't believe. Hi. Life changes here. Small things only.
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