Mathematika, ISSN 0025-5793, 2016, Volume 62, Issue 2, pp. 524 - 550

In this paper, we investigate in various ways the representation of a large natural number as a sum of a fixed power of Piatetski‐Shapiro numbers, thereby...

11P55 | 11L15 | 11L07 | 11B83 (secondary) | 11P05 (primary)

11P55 | 11L15 | 11L07 | 11B83 (secondary) | 11P05 (primary)

Journal Article

The American Mathematical Monthly, ISSN 0002-9890, 08/2019, Volume 126, Issue 7, pp. 651 - 654

Power sums were studied by many eminent mathematicians. But even now, there are still interesting open problems in this area. One of them is to characterize...

MSC: Primary 11B83 | MATHEMATICS | MSC | Mathematics - Number Theory

MSC: Primary 11B83 | MATHEMATICS | MSC | Mathematics - Number Theory

Journal Article

Quarterly Journal of Mathematics, ISSN 0033-5606, 03/2015, Volume 66, Issue 4, pp. 1127 - 1138

We prove that for 1 < c < 4/3 the subsequence of the Thue-Morse sequence t indexed by left perpendicularn(c)right perpendicular defines a normal sequence, that...

MATHEMATICS | Mathematics - Number Theory

MATHEMATICS | Mathematics - Number Theory

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 10/2015, Volume 268, pp. 844 - 858

In the paper, by induction, the Faà di Bruno formula, and some techniques in the theory of complex functions, the author finds explicit formulas for higher...

Bell polynomial of the second kind | Tangent number | Bernoulli number | Explicit formula | Derivative polynomial | Euler polynomial | MATHEMATICS, APPLIED | BERNOULLI NUMBERS | INEQUALITIES | IDENTITIES | COMPLETE MONOTONICITY | STIRLING NUMBERS | POLYNOMIALS | EXPLICIT FORMULAS | INTEGRAL-REPRESENTATION | 2ND KIND | 1ST KIND

Bell polynomial of the second kind | Tangent number | Bernoulli number | Explicit formula | Derivative polynomial | Euler polynomial | MATHEMATICS, APPLIED | BERNOULLI NUMBERS | INEQUALITIES | IDENTITIES | COMPLETE MONOTONICITY | STIRLING NUMBERS | POLYNOMIALS | EXPLICIT FORMULAS | INTEGRAL-REPRESENTATION | 2ND KIND | 1ST KIND

Journal Article

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, ISSN 0035-7596, 2018, Volume 48, Issue 7, pp. 2163 - 2174

Let E be an elliptic curve over Q described by y(2) = x(3)+Kx+L, where K, L is an element of Q. A set of rational points (x(i), y(i)) is an element of E(Q) for...

MATHEMATICS | sequences of consecutive cubes | ARITHMETIC PROGRESSIONS | Elliptic curves | rational points

MATHEMATICS | sequences of consecutive cubes | ARITHMETIC PROGRESSIONS | Elliptic curves | rational points

Journal Article

Experimental Mathematics, ISSN 1058-6458, 01/2018, Volume 27, Issue 1, pp. 100 - 110

The Collatz conjecture (also known as the 3x + 1 problem) concerns the behavior of the discrete dynamical system on the positive integers defined by iteration...

Secondary 60G40, 60G50, 11Y99 | random walk | 3 x + 1 | Primary 11B83 | Collatz conjecture | discrete dynamical system

Secondary 60G40, 60G50, 11Y99 | random walk | 3 x + 1 | Primary 11B83 | Collatz conjecture | discrete dynamical system

Journal Article

Analele Universitatii "Ovidius" Constanta - Seria Matematica, ISSN 1224-1784, 12/2019, Volume 27, Issue 3, pp. 25 - 35

We deduce exact integral formulae for the coefficients of Gaussian, multinomial and Catalan polynomials. The method used by the authors in the papers [2, 3, 4]...

Gaussian polynomial | Primary 11B83 | integral formula | multinomial polynomial | polygonal polynomial | Catalan polynomial | Secondary 26C05 | MATHEMATICS | MATHEMATICS, APPLIED

Gaussian polynomial | Primary 11B83 | integral formula | multinomial polynomial | polygonal polynomial | Catalan polynomial | Secondary 26C05 | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Mathematika, ISSN 0025-5793, 01/2011, Volume 57, Issue 1, pp. 41 - 49

In this paper, we study how close the terms of a finite arithmetic progression can get to a perfect square. The answer depends on the initial term, the common...

11D75 (primary) | 11J25 | 11B83 | 11L05 (secondary) | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Number Theory

11D75 (primary) | 11J25 | 11B83 | 11L05 (secondary) | MATHEMATICS | MATHEMATICS, APPLIED | Mathematics - Number Theory

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 1/2019, Volume 113, Issue 1, pp. 1 - 9

In the paper, the authors discuss the Bell polynomials and a sequence of polynomials applied to the theory of differential equations. Concretely speaking, the...

Faà di Bruno formula | 11C08 | Generating function | Secondary 11B73 | Differential equation | Theoretical, Mathematical and Computational Physics | 33B10 | Mathematics | Bell polynomial | Explicit formula | Primary 11B83 | Derivative | Mathematics, general | 26A06 | Applications of Mathematics | Identity | 26A09 | Stirling number | INEQUALITIES | Faa di Bruno formula | TERMS | DIAGONAL RECURRENCE RELATIONS | STIRLING NUMBERS | MATHEMATICS | 2ND KIND | Functions (mathematics) | Polynomials | Mathematical analysis | Combinatorial analysis | Differential equations | Identities

Faà di Bruno formula | 11C08 | Generating function | Secondary 11B73 | Differential equation | Theoretical, Mathematical and Computational Physics | 33B10 | Mathematics | Bell polynomial | Explicit formula | Primary 11B83 | Derivative | Mathematics, general | 26A06 | Applications of Mathematics | Identity | 26A09 | Stirling number | INEQUALITIES | Faa di Bruno formula | TERMS | DIAGONAL RECURRENCE RELATIONS | STIRLING NUMBERS | MATHEMATICS | 2ND KIND | Functions (mathematics) | Polynomials | Mathematical analysis | Combinatorial analysis | Differential equations | Identities

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 06/2018, Volume 68, Issue 3, pp. 527 - 536

We define a truncated Euler polynomial ) as a generalization of the classical Euler polynomial ). In this paper we give its some properties and relations with...

Secondary 11B83, 11B37, 05A15, 05A19 | truncated Euler polynomials | Bernoulli polynomials | Primary 11B68 | Euler polynomials | hypergeometric Bernoulli polynomials | Polynomials

Secondary 11B83, 11B37, 05A15, 05A19 | truncated Euler polynomials | Bernoulli polynomials | Primary 11B68 | Euler polynomials | hypergeometric Bernoulli polynomials | Polynomials

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 2/2019, Volume 48, Issue 2, pp. 445 - 458

The Fourier coefficients of powers of the Dedekind eta function can be studied simultaneously. The vanishing of the coefficients varies from super lacunary...

Cyclotomic polynomials | Secondary 11F30 | Functions of a Complex Variable | 11P84 | Field Theory and Polynomials | Mathematics | Fourier coefficients | 11F20 | Dedekind eta function | Primary 11D10 | 11R18 | Fourier Analysis | 11B83 | Integer-valued polynomials | Number Theory | Combinatorics | MATHEMATICS

Cyclotomic polynomials | Secondary 11F30 | Functions of a Complex Variable | 11P84 | Field Theory and Polynomials | Mathematics | Fourier coefficients | 11F20 | Dedekind eta function | Primary 11D10 | 11R18 | Fourier Analysis | 11B83 | Integer-valued polynomials | Number Theory | Combinatorics | MATHEMATICS

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 4/2019, Volume 157, Issue 2, pp. 522 - 536

Let n be a positive integer. Theisinger [7] proved that if $${n\ge 2}$$ n ≥ 2 , then the n-th harmonic sum $${\sum_{k=1}^n\frac{1}{k}}$$ ∑ k = 1 n 1 k is not...

reciprocal power sum | 11B83 | Bertrand’s postulate | Mathematics, general | 11B75 | Mathematics | integrality | 11B25 | arithmetic progression | primary 11N13 | p -adic valuation | p-adic valuation | MATHEMATICS | Bertrand's postulate | ELEMENTARY SYMMETRIC FUNCTIONS | Valuation

reciprocal power sum | 11B83 | Bertrand’s postulate | Mathematics, general | 11B75 | Mathematics | integrality | 11B25 | arithmetic progression | primary 11N13 | p -adic valuation | p-adic valuation | MATHEMATICS | Bertrand's postulate | ELEMENTARY SYMMETRIC FUNCTIONS | Valuation

Journal Article

Acta Mathematica Hungarica, ISSN 0236-5294, 2/2018, Volume 154, Issue 1, pp. 147 - 186

We extend Wolstenholme’s theorem to hyperharmonic numbers. Then, we obtain infinitely many congruence classes for hyperharmonic numbers using combinatorial...

5A10 | primary 11B83 | congruence identity | Mathematics, general | 11B75 | Mathematics | hyperharmonic number | harmonic number | MATHEMATICS | SPECIAL VALUES | ZETA-FUNCTION

5A10 | primary 11B83 | congruence identity | Mathematics, general | 11B75 | Mathematics | hyperharmonic number | harmonic number | MATHEMATICS | SPECIAL VALUES | ZETA-FUNCTION

Journal Article

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, 10/2019, Volume 113, Issue 4, pp. 3359 - 3367

In this paper, we introduce the degenerate central factorial polynomials and numbers of the second kind which are degenerate versions of the central factorial...

Secondary 11B75 | Primary 11B83 | Theoretical, Mathematical and Computational Physics | Degenerate central factorial polynomials of the second kind | Degenerate central factorial numbers of the second kind | Mathematics, general | Mathematics | Applications of Mathematics | MATHEMATICS | Polynomials | Combinatorial analysis

Secondary 11B75 | Primary 11B83 | Theoretical, Mathematical and Computational Physics | Degenerate central factorial polynomials of the second kind | Degenerate central factorial numbers of the second kind | Mathematics, general | Mathematics | Applications of Mathematics | MATHEMATICS | Polynomials | Combinatorial analysis

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 02/2017, Volume 67, Issue 1, pp. 51 - 70

In this paper, with reference to the previous work [WITUŁA, R.—SŁOTA, D.: , Appl. Anal. Discrete Math. (2009), 310–329] concerning the, so called, -Fibonacci...

Primary 11B39 | 11B83 | Fibonacci numbers | Lucas numbers | δ-Fibonacci numbers | MATHEMATICS | delta-Fibonacci numbers | Transformations (mathematics) | Polynomials

Primary 11B39 | 11B83 | Fibonacci numbers | Lucas numbers | δ-Fibonacci numbers | MATHEMATICS | delta-Fibonacci numbers | Transformations (mathematics) | Polynomials

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 10/2013, Volume 439, Issue 7, pp. 1700 - 1715

We approach Riordan arrays and their generalizations via umbral symbolic methods. This new approach allows us to derive fundamental aspects of the theory of...

Riordan arrays | Abelʼs identity | Umbral calculus | Abel's identity | MATHEMATICS, APPLIED | IDENTITIES | NUMBERS | CUMULANTS | CLASSICAL UMBRAL CALCULUS | Mathematics - Combinatorics

Riordan arrays | Abelʼs identity | Umbral calculus | Abel's identity | MATHEMATICS, APPLIED | IDENTITIES | NUMBERS | CUMULANTS | CLASSICAL UMBRAL CALCULUS | Mathematics - Combinatorics

Journal Article

Israel Journal of Mathematics, ISSN 0021-2172, 06/2017, Volume 220, Issue 2, pp. 691 - 738

We prove that the Thue-Morse sequence t along subsequences indexed by left perpendicularn(c)right perpendicular is normal, where 1 < c < 3/2. That is, for c in...

MATHEMATICS | N(C) | PRIME-NUMBERS | DIGITS | C-GREATER-THAN-1 | LARGE SIEVE | SUMS | Sequences (Mathematics) | Gaussian distribution | Research | Mathematical research | Mathematics - Number Theory

MATHEMATICS | N(C) | PRIME-NUMBERS | DIGITS | C-GREATER-THAN-1 | LARGE SIEVE | SUMS | Sequences (Mathematics) | Gaussian distribution | Research | Mathematical research | Mathematics - Number Theory

Journal Article

Periodica Mathematica Hungarica, ISSN 0031-5303, 03/2019, Volume 78, Issue 1, pp. 110 - 127

In the paper, the authors present several new relations and applications for the combinatorial sequence that counts the possible partitions of a finite set...

Lonesum matrices | Combinatorial identities | S-restricted Stirling numbers | Poly-Bernoulli numbers | Generating functions | MATHEMATICS, APPLIED | Secondary 11B73 | NUMBERS | CAUCHY | INCOMPLETE POLY-BERNOULLI | MATHEMATICS | Primary 11B83 | 05A19 | 05A15 | COMBINATORICS | Social service

Lonesum matrices | Combinatorial identities | S-restricted Stirling numbers | Poly-Bernoulli numbers | Generating functions | MATHEMATICS, APPLIED | Secondary 11B73 | NUMBERS | CAUCHY | INCOMPLETE POLY-BERNOULLI | MATHEMATICS | Primary 11B83 | 05A19 | 05A15 | COMBINATORICS | Social service

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 12/2018, Volume 187, Issue 4, pp. 705 - 728

In $$\mathbb {F}_q$$ Fq , Dartyge and Sárközy introduced the notion of digits and studied some properties of the sum of digits function. We will provide sharp...

Finite fields | Squares | Primitive elements | 11B83 | Digits | Sum of digits | Character sums | Mathematics, general | Mathematics | Primary 11A63 | Secondary 11T23 | MATHEMATICS | EXPONENTIAL-SUMS | Number Theory

Finite fields | Squares | Primitive elements | 11B83 | Digits | Sum of digits | Character sums | Mathematics, general | Mathematics | Primary 11A63 | Secondary 11T23 | MATHEMATICS | EXPONENTIAL-SUMS | Number Theory

Journal Article

SpringerPlus, ISSN 2193-1801, 12/2016, Volume 5, Issue 1, pp. 1 - 20

In the paper, the authors find some properties of the Catalan numbers, the Catalan function, and the Catalan–Qi function which is a generalization of the...

26A51 | Secondary 05A10 | Science | 44A20 | Complete monotonicity | 33C05 | Catalan function | 11Y55 | 11B83 | Ratio of gamma functions | 26A48 | Property | Logarithmically complete monotonicity | Science, general | Primary 33B15 | 05A20 | Catalan–Qi function | Minimality | Logarithmic convexity | Asymptotic expansion | Catalan number | 05A19 | 11Y60 | 05A16 | Integral representation | 05A15 | 26D15 | Inequality | MULTIDISCIPLINARY SCIENCES | Catalan-Qi function

26A51 | Secondary 05A10 | Science | 44A20 | Complete monotonicity | 33C05 | Catalan function | 11Y55 | 11B83 | Ratio of gamma functions | 26A48 | Property | Logarithmically complete monotonicity | Science, general | Primary 33B15 | 05A20 | Catalan–Qi function | Minimality | Logarithmic convexity | Asymptotic expansion | Catalan number | 05A19 | 11Y60 | 05A16 | Integral representation | 05A15 | 26D15 | Inequality | MULTIDISCIPLINARY SCIENCES | Catalan-Qi function

Journal Article

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