TY - JOUR
T1 - The spin of prime ideals
AU - Friedlander, J. B.
AU - Iwaniec, Henryk
AU - Mazur, B.
AU - Rubin, K.
PY - 2013/1/1
Y1 - 2013/1/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00222-012-0438-8
DO - 10.1007/s00222-012-0438-8
M3 - Article
AN - SCOPUS:84882833420
VL - 193
SP - 697
EP - 749
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
SN - 0020-9910
IS - 3
ER -