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Displaying 1601 – 1620 of 3014

On the Birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields

Matteo Longo (2006)

Annales de l’institut Fourier

Let $E / F$ be a modular elliptic curve defined over a totally real number field $F$ and let $φ$ be its associated eigenform. This paper presents a new method, inspired by a recent work of Bertolini and Darmon, to control the rank of $E$ over suitable quadratic imaginary extensions $K / F$ . In particular, this argument can also be applied to the cases not covered by the work of Kolyvagin and Logachëv, that is, when $[F : ℚ]$ is even and $φ$ not new at any prime.

On the bi-unitary analogues of Euler's arithmetical function and the gcd-sum function.

Tóth, László (2009)

Journal of Integer Sequences [electronic only]

On the Bombieri-Korobov estimate for Weyl sums

Scott T. Parsell (2009)

Acta Arithmetica

On the Boundedness of Weyl Sums.

Peter Hellekalek (1992)

Monatshefte für Mathematik

On the branch order of the ring of integers of an abelian number field

Kurt Girstmair (1992)

Acta Arithmetica

On the Brauer-Manin obstruction for zero-cycles on curves

Dennis Eriksson, Victor Scharaschkin (2008)

Acta Arithmetica

On the Brocard-Ramanujan problem and generalizations

Andrzej Dąbrowski (2012)

Colloquium Mathematicae

Let $p_{i}$ denote the ith prime. We conjecture that there are precisely 28 solutions to the equation $n ² - 1 = p ₁^{α ₁} \dots p_{k}^{α_{k}}$ in positive integers n and α₁,..., $α_{k}$ . This conjecture implies an explicit description of the set of solutions to the Brocard-Ramanujan equation. We also propose another variant of the Brocard-Ramanujan problem: describe the set of solutions in non-negative integers of the equation n! + A = x₁²+x₂²+x₃² (A fixed).

On the Brun-Titchmarsh theorem.

Christopher Hooley (1972)

Journal für die reine und angewandte Mathematik

On the Brun-Titchmarsh theorem

James Maynard (2013)

Acta Arithmetica

The Brun-Titchmarsh theorem shows that the number of primes which are less than x and congruent to a modulo q is less than (C+o(1))x/(ϕ(q)logx) for some value C depending on logx/logq. Different authors have provided different estimates for C in different ranges for logx/logq, all of which give C>2 when logx/logq is bounded. We show that one can take C=2 provided that logx/logq ≥ 8 and q is sufficiently large. Moreover, we also produce a lower bound of size $x / (q^{1 / 2} ϕ (q))$ when logx/logq ≥ 8 and is bounded....

On the canonical height for the algebraic unit group.

G.R. Everest (1992)

Journal für die reine und angewandte Mathematik

On the Carlitz problem on the number of solutions to some special equations over finite fields

Ioulia N. Baoulina (2011)

Journal de Théorie des Nombres de Bordeaux

We consider an equation of the type $a_{1}^{} x_{1}^{2} + \dots + a_{n}^{} x_{n}^{2} = b x_{1} \dots x_{n}$ over the finite field $𝔽_{q} = 𝔽_{p^{s}}$ . Carlitz obtained formulas for the number of solutions to this equation when $n = 3$ and when $n = 4$ and $q \equiv 3 (mod 4)$ . In our earlier papers, we found formulas for the number of solutions when $d = gcd (n - 2, (q - 1) / 2) = 1$ or $2$ or $4$ ; and when $d > 1$ and $- 1$ is a power of $p$ modulo $2 d$ . In this paper, we obtain formulas for the number of solutions when $d = 2^{t}$ , $t \geq 3$ , $p \equiv 3 or 5 (mod 8)$ or $p \equiv 9 (mod 16)$ . For general case, we derive lower bounds for the number of solutions.

On the Catalan equation over algebraic number fields.

B. Brindza, K. Györy, R. Tijdeman (1986)

Journal für die reine und angewandte Mathematik

On the center of Galois groups of maximal pro-p extensions of algebraic number fields with restricted ramification.

Masakazu Yamagishi (1993)

Journal für die reine und angewandte Mathematik

On the central coefficients of Bell matrices.

Barry, Paul (2011)

Journal of Integer Sequences [electronic only]

On the central limit theorem for random variables related to the continued fraction expansion

C. Faivre (1996)

Colloquium Mathematicae

On the changes of sign of a certain class of error functions

J. Proschan (1971)

Acta Arithmetica

On the characteristic power series of the U operator

Fernando Q. Gouvêa, Barry Mazur (1993)

Annales de l'institut Fourier

We show that the coefficients of the characteristic power series of Atkin’s U operator acting on overconvergent $p$ -adic modular forms of weight $k$ vary $p$ -adically continuously as functions of $k$ . Are they in fact Iwasawa functions of $k$ ?

Currently displaying 1601 – 1620 of 3014

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Displaying 1601 – 1620 of 3014

On the Birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields

On the bi-unitary analogues of Euler's arithmetical function and the gcd-sum function.

On the Bombieri-Korobov estimate for Weyl sums

On the Boundedness of Weyl Sums.

On the branch order of the ring of integers of an abelian number field

On the Brauer-Manin obstruction for zero-cycles on curves

On the Brocard-Ramanujan problem and generalizations

On the Brun-Titchmarsh theorem.

On the Brun-Titchmarsh theorem

On the canonical height for the algebraic unit group.

On the Carlitz problem on the number of solutions to some special equations over finite fields

On the Catalan equation over algebraic number fields.

On the center of Galois groups of maximal pro-p extensions of algebraic number fields with restricted ramification.

On the central coefficients of Bell matrices.

On the central limit theorem for random variables related to the continued fraction expansion

On the changes of sign of a certain class of error functions

On the characteristic power series of the U operator

On the Chow groups of quadratic Grassmannians.

On the circle problem with general weight

On the circle problem with polynomial weight

Currently displaying 1601 – 1620 of 3014