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Is there a simple relation between the theta series of lattices that are neighbors in the sense of Kneser? In many articles (Nebe, Andrianov etc) there is a connection claimed with the Hecke operator but this is never clear enough and always in high degree ( I modestly would like to see such a relation in degree (aka genus) ONE.

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welcome to mathoverflow :) – Dima Pasechnik Nov 26 '12 at 11:25
    
Even simpler question: can you say when two neighbors have the same number of roots? – Giulio Sep 25 '14 at 11:24

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