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Displaying 1681 – 1700 of 3028

On the conductor formula of Bloch

Kazuya Kato, Takeshi Saito (2004)

Publications Mathématiques de l'IHÉS

In [6], S. Bloch conjectures a formula for the Artin conductor of the ℓ-adic etale cohomology of a regular model of a variety over a local field and proves it for a curve. The formula, which we call the conductor formula of Bloch, enables us to compute the conductor that measures the wild ramification by using the sheaf of differential 1-forms. In this paper, we prove the formula in arbitrary dimension under the assumption that the reduced closed fiber has normal crossings.

On the conductor of the Jacobi sum Hecke character

Hiroo Miki (1994)

Compositio Mathematica

On the congruence $a_{1} {(x_{1})}^{k} + . . . + a_{s} {(x_{s})}^{k} = N (m o d p^{n})$

J. Bovey (1973)

Acta Arithmetica

On the congruence $a x + b y \equiv 1$ modulo $x y$ .

Brzeziński, J., Holsztyński, W., Kurlberg, P. (2005)

Experimental Mathematics

On the congruence $f (x^{k}) \equiv 0 m o d q$ , where q is a prime and f is a polynomial

J. Wójcik (1988)

Acta Arithmetica

On the congruence $f (x^{k}) \equiv 0 m o d q$ , where q is a prime and f is a k-normal polynomial

J. Wójcik (1982)

Acta Arithmetica

On the congruence f(x) + g(y) + c ≡ 0 (mod xy) (completion of Mordell's proof)

A. Schinzel (2015)

Acta Arithmetica

Assertions on the congruence f(x) + g(y) + c ≡ 0 (mod xy) made without proof by Mordell in his paper in Acta Math. 88 (1952) are either proved or disproved.

On the congruence $N \equiv A (mod ϕ (N))$ .

Banks, William D., Güloğlu, Ahmet M., Nevans, C.Wesley (2008)

Integers

On the congruence subgroup problem

Madabusi S. Raghunathan (1976)

Publications Mathématiques de l'IHÉS

On the congruences $σ (n) \equiv a (m o d n)$ and $n \equiv a (m o d φ (n))$

Carl Pomerance (1975)

Acta Arithmetica

On the congruence-subgroup problem for some anisotropic algebraic groups over number fields.

G. Tomanov (1989)

Journal für die reine und angewandte Mathematik

On the Conjecture of Birch and Swinnerton-Dyer

J. Coates, A. Wiles (1977)

Inventiones mathematicae

On the conjecture of Birch and Swinnerton-Dyer for abelian varieties over function fields in characteristic p > 0.

Werner Bauer (1992)

Inventiones mathematicae

On the conjecture of Lichtenbaum and of Chinburg over function fields.

Sunghan Bae (1989)

Mathematische Annalen

On the conjectures of Birch and Swinnerton-Dyer and a geometric analog

John Tate (1964/1966)

Séminaire Bourbaki

On the conjectures of Mordell and Lang in positive characteristics.

J.F. Voloch (1991)

Inventiones mathematicae

On the conjectures of Rauzy and Shallit for infinite words

Jean-Paul Allouche, Mireille Bousquet-Mélou (1995)

Commentationes Mathematicae Universitatis Carolinae

We show a connection between a recent conjecture of Shallit and an older conjecture of Rauzy for infinite words on a finite alphabet. More precisely we show that a Rauzy-like conjecture is equivalent to Shallit's. In passing we correct a misprint in Rauzy's conjecture.

On the constant factor in Vinogradov's Mean Value Theorem

Géza Kós (2001)

Acta Arithmetica

On the constant β(k) in Rosser's sieve

R. Hall (1977)

Acta Arithmetica

On the construction of dense lattices with a given automorphisms group

Philippe Gaborit, Gilles Zémor (2007)

Annales de l’institut Fourier

We consider the problem of constructing dense lattices in $ℝ^{n}$ with a given non trivial automorphisms group. We exhibit a family of such lattices of density at least $c n 2^{- n}$ , which matches, up to a multiplicative constant, the best known density of a lattice packing. For an infinite sequence of dimensions $n$ , we exhibit a finite set of lattices that come with an automorphisms group of size $n$ , and a constant proportion of which achieves the aforementioned lower bound on the largest packing density. The algorithmic...

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