From monoids to hyperstructures: in search of an absolute arithmetic

Details From monoids to hyperstructures: in search of an absolute arithmetic From monoids to hyperstructures: in search of an absolute arithmetic

2010-06-24

arxiv.org/abs/1006.4810v1

Mathematics

Algebraic Geometry

43 pages, 1 figure

Scientific paper

We show that the trace formula interpretation of the explicit formulas expresses the counting function N(q) of the hypothetical curve C associated to the Riemann zeta function, as an intersection number involving the scaling action on the adele class space. Then, we discuss the algebraic structure of the adele class space both as a monoid and as a hyperring. We construct an extension R^{convex} of the hyperfield S of signs, which is the hyperfield analogue of the semifield R_+^{max} of tropical geometry, admitting a one parameter group of automorphisms fixing S. Finally, we develop function theory over Spec(S) and we show how to recover the field of real numbers from a purely algebraic construction, as the function theory over Spec(S).

Affiliated with

Also associated with

No associations

Rating

From monoids to hyperstructures: in search of an absolute arithmetic does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with From monoids to hyperstructures: in search of an absolute arithmetic, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and From monoids to hyperstructures: in search of an absolute arithmetic will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-676177