Starting with gaps between k-free numbers

DOI10.1142/S1793042115400199zbMath1333.11091WikidataQ114072038 ScholiaQ114072038MaRDI QIDQ2942518

Ognian Trifonov, Michael Filaseta, Sidney W. Graham

Publication date: 11 September 2015

Published in: International Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

lattice pointscurvesgapsshort intervals\(k\)-free numbers

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Lattice points in specified regions (11P21) Distribution of integers with specified multiplicative constraints (11N25) Small fractional parts of polynomials and generalizations (11J54) Primes represented by polynomials; other multiplicative structures of polynomial values (11N32)

Related Items (3)

Explicit bounds for large gaps between squarefree integers ⋮ Bounding the number of lattice points near a convex curve by curvature ⋮ The distribution of $k$-free numbers

Cites Work

• Power-free values of polynomials
• Integer points in the neighborhood of a plane curve of class \(C^n\). II
• Short interval results for squarefree numbers
• On the power-free values of polynomials in two variables. II
• On the method of Thue-Siegel
• On the Diophantine equation \(y^2=4q^n+4q+1\)
• The diophantine equation \(x^ 2=4q^{a/2}+4q+1\), with an application to coding theory
• An elementary approach to short interval results for \(k\)-free numbers
• Powerfree values of binary forms
• Ein Beweis des Thue-Siegelschen Satzes über die Approximation algebraischer Zahlen für binomische Gleichungen
• Applications of the hypergeometric method to the generalized Ramanujan-Nagell equation
• The number of lattice points on a convex curve
• On gaps between \(k\)-free numbers
• The number of integral points on arcs and ovals
• Die Gleichung \(ax^n-by^n=c\)
• Rational approximation to algebraic numbers of small height: the Diophantine equation |axn - byn|= 1
• On square-full integers in a short interval
• On the distribution of gaps between squarefree numbers
• LATTICE POINTS CLOSE TO A SMOOTH CURVE AND SQUAREFULL NUMBERS IN SHORT INTERVALS
• Solving a family of Thue equations with an application to the equation x²-Dy⁴=1
• The Probability that the Number of Groups of Squarefree Order is Two More than a Fixed Prime
• On square-full numbers in short intervals
• Counting Rational Points on Algebraic Varieties
• Yet another generalization of the Ramanujan–Nagell equation
• Power Free Values of Polynomials III
• On the number of square‐full integers between successive squares
• Die Werteverteilung der Anzahl der nicht-isomorphen ABELschen Gruppen endlicher Ordnung in kurzen Intervallen
• On the Number of Finite Non‐isomorphic Abelian Groups in Short Intervals
• Square-full numbers in short intervals
• POWER-FREE VALUES OF BINARY FORMS
• On Gaps Between Squarefree Numbers II
• The large sieve
• Power free values of polynomials
• Power Free Values of Polynomials II
• Fractional parts of powers of rational numbers
• Explicit Lower Bounds for Rational Approximation to Algebraic Numbers
• Estimates of the least prime factor of a binomial coefficient
• On the number of finite non-isomorphic Abelian groups in short intervals
• The Distribution of Fractional Parts with Applications to Gap Results in Number Theory
• Ricerche aritmetiche sui polinomi
• The square-full numbers in an interval
• Primes in arithmetic progressions
• Simultaneous rational approximation to binomial functions
• Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients
• POWER-FREE VALUES OF POLYNOMIALS
• Rational Approximations to Certain Algebraic Numbers
• On the power free values of polynomials
• RATIONAL APPROXIMATIONS TO 23 AND OTHER ALGEBRAIC NUMBERS
• On the Gaps between Squarefree Numbers
• On the Gaps between Consecutive k -Free Integers
• Arithmetical Properties of Polynomials
• On the Difference between Consecutive Squarefree Numbers
• VAN DER CORPUT'S METHOD AND THE THEORY OF EXPONENT PAIRS
• On the Distribution of Square-Free Numbers
• On the number of solutions of simultaneous Pell equations

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