I find an explicit description of modular units in terms of Siegel functions for the modular curves X+ ns(pk) associated to the normalizer of a non-split Cartan subgroup of level pk where p 6= 2,3 is a prime. The Cuspidal Divisor Class Group C+ ns(pk) on X+ ns(pk) is explicitly described as a module over the group ring R = Z[(Z/pkZ)∗/{±1}]. In this thesis I give a formula involving generalized Bernoulli numbers B2,χ for |C+ ns(pk)| and estimate the order ofgrowth of |C+ ns(p)|. I study the p−primary part of the Cuspidal Divisor ClassGroup at level p.
Cuspidal divisor class groups of non-split cartan modular curves
CARLUCCI, PIERFRANCESCO
2015
Abstract
I find an explicit description of modular units in terms of Siegel functions for the modular curves X+ ns(pk) associated to the normalizer of a non-split Cartan subgroup of level pk where p 6= 2,3 is a prime. The Cuspidal Divisor Class Group C+ ns(pk) on X+ ns(pk) is explicitly described as a module over the group ring R = Z[(Z/pkZ)∗/{±1}]. In this thesis I give a formula involving generalized Bernoulli numbers B2,χ for |C+ ns(pk)| and estimate the order ofgrowth of |C+ ns(p)|. I study the p−primary part of the Cuspidal Divisor ClassGroup at level p.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
Tesi PhD di Pierfrancesco Carlucci.pdf
non disponibili
Dimensione
569.92 kB
Formato
Adobe PDF
|
569.92 kB | Adobe PDF |
I documenti in UNITESI sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
Utilizza questo identificativo per citare o creare un link a questo documento:
https://hdl.handle.net/20.500.14242/195542
Il codice NBN di questa tesi è
URN:NBN:IT:UNIROMA2-195542