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Displaying 501 – 520 of 3028

On blocks of arithmetic progressions with equal products

N. Saradha (1997)

Journal de théorie des nombres de Bordeaux

Let $f (X) \in ℚ [X]$ be a monic polynomial which is a power of a polynomial $g (X) \in ℚ [X]$ of degree $μ \geq 2$ and having simple real roots. For given positive integers $d_{1}, d_{2}, ℓ, m$ with $ℓ < m$ and gcd $(ℓ, m) = 1$ with $μ \leq m + 1$ whenever $m < 2$ , we show that the equation $f (x) f (x + d_{1}) \dots f (x + (ℓ k - 1) d_{1}) = f (y) f (y + d_{2}) \dots f (y + (m k - 1) d_{2})$ with $f (x + j d_{1}) \neq 0$ for $0 \leq j < ℓ k$ has only finitely many solutions in integers $x, y$ and $k \geq 1$ except in the case $m = μ = 2, ℓ = k = d_{2} = 1, f (X) = g (X), x = f (y) + y .$

On Bombieri's asymptotic sieve

John Friedlander, Henryk Iwaniec (1978)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

On Bombieri's estimate for exponential sums

J. Chalk, R. Smith (1971)

Acta Arithmetica

On Bourgain's bound for short exponential sums and squarefree numbers

Ramon M. Nunes (2016)

Acta Arithmetica

We use Bourgain's recent bound for short exponential sums to prove certain independence results related to the distribution of squarefree numbers in arithmetic progressions.

On Bröcker's t-invariant and separating families for constructible sets.

M. Marshall (1994)

Aequationes mathematicae

On Bumby’s equation ${(x^{2} - 2)}^{2} - 2 = 2 y^{2}$ : a solution via pythagorean triples

Ladislav Beran (1987)

Acta Universitatis Carolinae. Mathematica et Physica

On canonical and quasi-canonical liftings.

B.H. Gross (1986)

Inventiones mathematicae

On canonical subfield preserving polynomials

Giacomo Micheli, Davide Schipani (2014)

Acta Arithmetica

Explicit monoid structure is provided for the class of canonical subfield preserving polynomials over finite fields. Some classical results and asymptotic estimates will follow as corollaries.

On Cantor's singular moments.

Prodinger, H. (2000)

Southwest Journal of Pure and Applied Mathematics [electronic only]

On Carlitz's type $q$ -Euler numbers associated with the fermionic $P$ -adic integral on $ℤ_{p}$ .

Kim, Min-Soo, Kim, Taekyun, Ryoo, Cheon-Seoung (2010)

Journal of Inequalities and Applications [electronic only]

On Catalan's problem

K. Inkeri (1964)

Acta Arithmetica

On certain additive representations of integers

Thanigasalam, K. (1983/1984)

Portugaliae mathematica

On certain algebraic curves related to polynomial maps

Patrick Morton (1996)

Compositio Mathematica

On certain algebraic groups attached to local number-fields.

T. Kambayashi (1975)

Journal für die reine und angewandte Mathematik

On Certain Approaches for Analysis and Design of Cryptographic Techniques

Miodrag Mihaljević (2012)

Zbornik Radova

On Certain Arithmetic Automorphic Forms for SU (1, q).

Stephen S. Kudla (1979)

Inventiones mathematicae

On certain arithmetic functions involving the greatest common divisor

Ekkehard Krätzel, Werner Nowak, László Tóth (2012)

Open Mathematics

The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ2(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.

Currently displaying 501 – 520 of 3028

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Displaying 501 – 520 of 3028

On blocks of arithmetic progressions with equal products

On Bombieri's asymptotic sieve

On Bombieri's estimate for exponential sums

On Bourgain's bound for short exponential sums and squarefree numbers

On Bröcker's t-invariant and separating families for constructible sets.

On Bumby’s equation ${(x^{2} - 2)}^{2} - 2 = 2 y^{2}$ : a solution via pythagorean triples

On canonical and quasi-canonical liftings.

On canonical subfield preserving polynomials

On Cantor's singular moments.

On Carlitz's type $q$ -Euler numbers associated with the fermionic $P$ -adic integral on $ℤ_{p}$ .

On Catalan's problem

On certain additive representations of integers

On certain algebraic curves related to polynomial maps

On certain algebraic groups attached to local number-fields.

On Certain Approaches for Analysis and Design of Cryptographic Techniques

On Certain Arithmetic Automorphic Forms for SU (1, q).

On certain arithmetic functions involving the greatest common divisor

On certain asymptotic functional equations.

On certain character sums

On Certain Classes of Sets of Natural Numbers

Currently displaying 501 – 520 of 3028