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Let $M (α)$ be the Mahler measure of an algebraic number $α$ , and $V$ be an open subset of $ℂ$ . Then its Lehmer constant $L (V)$ is inf $M {(α)}^{1 / deg (α)}$ , the infimum being over all non-zero non-cyclotomic $α$ lying with its conjugates outside $V$ . We evaluate $L (V)$ when $V$ is any annulus centered at $0$ . We do the same for a variant of $L (V)$ , which we call the transfinite Lehmer constant $L_{\infty} (V)$ .Also, we prove the converse to Langevin’s Theorem, which states that $L (V) > 1$ if $V$ contains a point of modulus $1$ . We prove the corresponding result for $L_{\infty} (V)$ .

The Lehmer strength bounds for total ramification

John Garza (2009)

Acta Arithmetica

The Lehmus inequality.

H.S.M. Coxeter (1985)

Aequationes mathematicae

The Length of Periodic Continued Fractions.

K.E. Hirst (1972)

Monatshefte für Mathematik

The level 1 weight 2 case of Serre's conjecture.

L. Dieulefait (2007)

Revista Matemática Iberoamericana

The level of distribution of the special values of L-functions

Ritabrata Munshi (2009)

Acta Arithmetica

The level of real projective spaces.

Stephan Stolz (1989)

Commentarii mathematici Helvetici

The L-function L3(s, ...) is entire.

C.J. Moreno, F. Shahidi (1985)

Inventiones mathematicae

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

Cornelius Greither, Radiu Kučera (2002)

Annales de l’institut Fourier

The so-called Lifted Root Number Conjecture is a strengthening of Chinburg’s $Ω (3)$ - conjecture for Galois extensions $K / F$ of number fields. It is certainly more difficult than the $Ω (3)$ -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. An important...

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The least prime in an arithmetic progression with prime difference.

The least prime primitive root and the shifted sieve

The least prime which does not split completely.

The least primitive root in number fields

The least square-free number in an arithmetic progression.

The Lefschetz number of an involution on the space of classes of positive definite quadratic forms.

The Lefschetz Number of an Involution on the Space of Harmonic Cusp Forms of SL3.

The Lehmer constants of an annulus

The Lehmer strength bounds for total ramification

The Lehmus inequality.

The Length of Periodic Continued Fractions.

The level 1 weight 2 case of Serre's conjecture.

The level of distribution of the special values of L-functions

The level of real projective spaces.

The L-function L3(s, ...) is entire.

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

The Lifted Root Number Conjecture for some cyclic extensions of ℚ

The Limit Shape of Convex Lattice Polygons.

The linear sieve, revisited

The Linnik conjecture. A local approach.

Currently displaying 601 – 620 of 1341