The spin of prime ideals

2011/10/28 by John Friedlander, Henryk Iwaniec, Friedlander, J. B. +5 · 3 citations
Mathematics · #11R44 (Primary) 11G05 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1110.6331

openalex publication_date 2011/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Fixing a nontrivial automorphism of a number field K, we associate to ideals in K an invariant (with values in 0,1,-1) that 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.

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• Parameters of solvable automorphic forms
• The spin of prime ideals and level-raising of even Galois representations
• A Hilbert 90 Property for S-Class Groups and Applications to the Gross--Kuz'min Conjecture

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