منابع مشابه
L-functions and Cyclotomic Units
Here RK is the regulator of K, wK is the number of roots of unity in K and hK is the class number of K. This formula is a striking connection between arithmetic and analysis, and there have been many attempts to generalize it to other L-functions: one expects that the value of a “motivic” L-function at an integer point should involve a transcendental factor, a boring rational factor, and an int...
متن کاملOn Modular Units
Introduction. In [6], Kubert and Lang describe the group of integral modular units on Γ(n) (“units over Z” in their terminology), and in particular determine its rank. Their method is based on finding explicit generators for the group of all modular units, and then by calculating their q-expansions to determine which are integral. In §5 of , Beilinson suggests another approach, based on represe...
متن کاملRoots of Modular Units
Let p be a prime. We prove that if a modular unit has a pth root that is again a modular unit, then the level of that root is at most p times the level of the original unit.
متن کاملCyclotomic Units and the Iwasawa Main Conjecture
In these notes, we follow the proof in [1] of the main conjecture of Iwasawa theory making heavy use of the Euler system of cyclotomic units. On the one hand, using the local theory of Coleman series and ideas of Iwasawa one obtains a connection with the p-adic zeta function. On the other hand by CFT and Rubin’s refinement of the ideas of Kolyvagin (and the analytic class number formula) one ob...
متن کاملClass invariants and cyclotomic unit groups from special values of modular units
In this article we obtain class invariants and cyclotomic unit groups by considering specializations of modular units. We construct these modular units from functional solutions to higher order q-recurrence equations given by Selberg in his work generalizing the Rogers-Ramanujan identities. As a corollary, we provide a new proof of a result of Zagier and Gupta, originally considered by Gauss, r...
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ژورنال
عنوان ژورنال: Bulletin de la Société mathématique de France
سال: 1979
ISSN: 0037-9484,2102-622X
DOI: 10.24033/bsmf.1890