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.
2015
Inglese
SCHOOF, RENATUS JOHANNES
Università degli Studi di Roma "Tor Vergata"
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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