## Displaying similar documents to “Special values of $L$-functions attached to ${X}_{1}\left(N\right)$”

### The lifted root number conjecture for fields of prime degree over the rationals: an approach via trees and Euler systems

Annales de l’institut Fourier

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The so-called Lifted Root Number Conjecture is a strengthening of Chinburg’s $\Omega \left(3\right)$- conjecture for Galois extensions $K/F$ of number fields. It is certainly more difficult than the $\Omega \left(3\right)$-localization. Following the lead of Ritter and Weiss, we prove the Lifted Root Number Conjecture for the case that $F=ℚ$ and the degree of $K/F$ is an odd prime, with another small restriction on ramification. The very explicit calculations with cyclotomic units use trees and some classical combinatorics for bookkeeping....

Acta Arithmetica

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Acta Arithmetica

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### Modular curves and unramified extensions of number fields

Compositio Mathematica

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### Jacobi-sum Hecke characters and Gauss-sum identities

Compositio Mathematica

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### Connections between ${B}_{2,\chi }$ for even quadratic Dirichlet characters $\chi$ and class numbers of appropriate imaginary quadratic fields, II

Compositio Mathematica

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Acta Arithmetica

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