The spin of prime ideals

J. B. Friedlander, Henryk Iwaniec, B. Mazur, K. Rubin

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Fixing a nontrivial automorphism of a number field K, we associate to ideals in K an invariant (with values in {0,±1}) which we call the spin and for which the associated L-function does not possess Euler products. We are nevertheless able, using the techniques of bilinear forms, to handle spin value distribution over primes, obtaining stronger results than the analogous ones which follow from the technology of L-functions in its current state. The initial application of our theorem is to the arithmetic statistics of Selmer groups of elliptic curves.

Original languageEnglish (US)
Pages (from-to)697-749
Number of pages53
JournalInventiones Mathematicae
Issue number3
StatePublished - Jan 1 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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