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Consider a recurrence sequence ${(x_{k})}_{k \in ℤ}$ of integers satisfying $x_{k + n} = a_{n - 1} x_{k + n - 1} + . . . + a ₁ x_{k + 1} + a ₀ x_{k}$ , where $a ₀, a ₁, . . ., a_{n - 1} \in ℤ$ are fixed and a₀ ∈ -1,1. Assume that $x_{k} > 0$ for all sufficiently large k. If there exists k₀∈ ℤ such that $x_{k ₀} < 0$ then for each negative integer -D there exist infinitely many rational primes q such that $q | x_{k}$ for some k ∈ ℕ and (-D/q) = -1.

Towards explicit description of ramification filtration in the 2-dimensional case

Victor Abrashkin (2004)

Journal de Théorie des Nombres de Bordeaux

The principal result of this paper is an explicit description of the structure of ramification subgroups of the Galois group of 2-dimensional local field modulo its subgroup of commutators of order $\geq 3$ . This result plays a clue role in the author’s proof of an analogue of the Grothendieck Conjecture for higher dimensional local fields, cf. Proc. Steklov Math. Institute, vol. 241, 2003, pp. 2-34.

Towards the Jacquet conjecture on the Local Converse Problem for $p$ -adic ${GL}_{n}$

Dihua Jiang, Chufeng Nien, Shaun Stevens (2015)

Journal of the European Mathematical Society

The Local Converse Problem is to determine how the family of the local gamma factors $γ (s, π \times τ, ψ)$ characterizes the isomorphism class of an irreducible admissible generic representation $π$ of ${GL}_{n} (F)$ , with $F$ a non-archimedean local field, where $τ$ runs through all irreducible supercuspidal representations of ${GL}_{r} (F)$ and $r$ runs through positive integers. The Jacquet conjecture asserts that it is enough to take $r = 1, 2, ..., [\frac{n}{2}]$ . Based on arguments in the work of Henniart and of Chen giving preliminary steps towards the Jacquet conjecture,...

Trace forms of central simple algebras.

D.W. Lewis (1994)

Mathematische Zeitschrift

Trace formula in noncommutative Geometry and the zeros of the Riemann zeta function

Alain Connes (1997)

Journées équations aux dérivées partielles

Trace formulae and applications to class numbers

Nicole Raulf (2014)

Open Mathematics

In this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL2( $𝒪_{K}$ ) with $𝒪_{K}$ being the ring of integers of an imaginary quadratic number field K of class number H K > 1. Furthermore, as a corollary we obtain an asymptotic result for class numbers of binary quadratic forms.

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Touchard polynomials, partial Bell polynomials and polynomials of binomial type.

Tournament sequences and Meeussen sequences.

Tours de corps de classes et estimations de discrimants.

Tours de corps de classes et estimations de discriminants.

Tours de Hilbert des extensions cubiques cycliques de Q.

Toward an arithmetic of polynomials.

Towards a General Theory of Formally ...-Adic Fields.

Towards a Katona type proof for the 2-intersecting Erdős-Ko-Rado theorem.

Towards a stable trace formula.

Towards Bauer's theorem for linear recurrence sequences

Towards explicit description of ramification filtration in the 2-dimensional case

Towards the Jacquet conjecture on the Local Converse Problem for $p$ -adic ${GL}_{n}$

Trace forms of central simple algebras.

Trace formula in noncommutative Geometry and the zeros of the Riemann zeta function

Trace formulae and applications to class numbers

Trace formulae and imaginary quadratic fields.

Trace formulas and class number sums

Trace functions and Galois invariant p-adic measures.

Trace maps in algebraic K-theory and the Coates-Wiles homomorphism.

Trace-compatible polynomial sequences over finite fields. (Spur-kompatible Polynomfolgen über endlichen Körpern.)

Currently displaying 1161 – 1180 of 1340