2016, ISBN 9780691170190, xiii, 229

We use addition on a daily basis--yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It...

Mathematics | Number theory | General | Counting & Numeration | Number Theory | Popular works

Mathematics | Number theory | General | Counting & Numeration | Number Theory | Popular works

Book

2013, Encyclopedia of mathematics and its applications, ISBN 9781107418578, Volume 150, xix, 368

"The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they...

MATHEMATICS / Number Theory | Number theory | Lattice theory | Mathematics

MATHEMATICS / Number Theory | Number theory | Lattice theory | Mathematics

Book

1990, Annals of mathematics studies, ISBN 9780691085999, Volume no. 124., ix, 430

Book

2016, ISBN 9783319282022, 552

This book collects more than thirty contributions in memory of Wolfgang Schwarz, most of which were presented at the seventh International Conference on...

Mathematics | Number theory | Sequences (Mathematics) | History of Mathematical Sciences | Number Theory | Sequences, Series, Summability

Mathematics | Number theory | Sequences (Mathematics) | History of Mathematical Sciences | Number Theory | Sequences, Series, Summability

eBook

2009, MAA guides, ISBN 9780883853474, Volume 5, x, 141

Book

2004, Mathematical Association of America, ISBN 9780521546775, x, 306

..., exponential sums, and the inequalities of Hölder, Hilbert, and Hardy. The text is accessible to anyone who knows calculus and who cares about solving problems. It is well suited to self-study, directed study, or as a supplement to courses in analysis, probability, and combinatorics.

Inequalities (Mathematics)

Inequalities (Mathematics)

Book

2011, London Mathematical Society student texts, ISBN 1107002532, Volume 76, xvii, 287

.... The many applications provided include applications to sums of squares, sums of triangular numbers, recurrence relations for divisor functions, convolution sums involving the divisor functions, and many others...

Liouville, Joseph, 1809-1882 | Number theory | Liouville, Joseph | 1809-1882

Liouville, Joseph, 1809-1882 | Number theory | Liouville, Joseph | 1809-1882

Book

2013, Discrete mathematics and its applications, ISBN 9781439873786, xxxv, 1033

"Preface The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference book for the theory and applications of nite elds. It is not...

COMPUTERS / Security / Cryptography | MATHEMATICS / Combinatorics | MATHEMATICS / Number Theory | Finite fields (Algebra)

COMPUTERS / Security / Cryptography | MATHEMATICS / Combinatorics | MATHEMATICS / Number Theory | Finite fields (Algebra)

Book

2018, 1st ed. 2018, ISBN 9783319746470, 168

This book develops the foundations of "summability calculus", which is a comprehensive theory of fractional finite sums...

Mathematical analysis | Finite differences | Fractional calculus | Ordinary Differential Equations | Special Functions | Sequences, Series, Summability | Approximations and Expansions | Mathematics | Number Theory | Real Functions | Series acceleration | Asymptotic expansions | Numerical integration | Bernoulli numbers | Euler-mascheroni constant | Divergent series | Gamma and polygamma functions | Euler-maclaurin summation formula | Analytic summability theory | Matrix summability methods | Riemann zeta function | Fractional finite sums | Special functions

Mathematical analysis | Finite differences | Fractional calculus | Ordinary Differential Equations | Special Functions | Sequences, Series, Summability | Approximations and Expansions | Mathematics | Number Theory | Real Functions | Series acceleration | Asymptotic expansions | Numerical integration | Bernoulli numbers | Euler-mascheroni constant | Divergent series | Gamma and polygamma functions | Euler-maclaurin summation formula | Analytic summability theory | Matrix summability methods | Riemann zeta function | Fractional finite sums | Special functions

eBook

2004, Colloquium publications, ISBN 9780821836330, Volume 53., xi, 615

Book

2012, University lecture series, ISBN 9780821853672, Volume 59, x, 190

Book

13.
Factors of Sums and Alternating Sums of Products of q-binomial Coefficients and Powers of q-integers

TAIWANESE JOURNAL OF MATHEMATICS, ISSN 1027-5487, 02/2019, Volume 23, Issue 1, pp. 11 - 27

..., where [n] = 1 + q + ... + q(n-1) and [(n)(k)] = Pi(k)(i=1) (1 - q(n-i+1))/(1-q(i)). This gives a q-analogue of some divisibility results of sums and alternating sums involving binomial coefficients and powers of integers obtained by Guo and Zeng...

MATHEMATICS | q-binomial coefficients | Q-ANALOGS | q-super Catalan numbers | cyclotomic polynomial | q-ballot numbers | CONGRUENCES | q-Catalan numbers

MATHEMATICS | q-binomial coefficients | Q-ANALOGS | q-super Catalan numbers | cyclotomic polynomial | q-ballot numbers | CONGRUENCES | q-Catalan numbers

Journal Article

2012, Graduate studies in mathematics, ISBN 0821889869, Volume 142., x, 187

Book

Discrete Applied Mathematics, ISSN 0166-218X, 07/2016, Volume 207, pp. 120 - 131

.... The total eccentricity of a tree, Ecc(T), is the sum of the eccentricities of its vertices...

Extremal problems | Degree sequence | Eccentricity | Greedy tree | Level-greedy tree | Greedy caterpillar | RATIOS | GRAPH | MATHEMATICS, APPLIED | EXTREMAL VALUES | MINIMAL NUMBER | DISTANCES | SUBTREES | AVERAGE ECCENTRICITY | WIENER INDEX | Trees | Leaves | Mathematical analysis | Invariants | Sums

Extremal problems | Degree sequence | Eccentricity | Greedy tree | Level-greedy tree | Greedy caterpillar | RATIOS | GRAPH | MATHEMATICS, APPLIED | EXTREMAL VALUES | MINIMAL NUMBER | DISTANCES | SUBTREES | AVERAGE ECCENTRICITY | WIENER INDEX | Trees | Leaves | Mathematical analysis | Invariants | Sums

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2014, Volume 272, Issue 1, pp. 201 - 226

We work out some formulas for nonlinear Euler sums involving multiple zeta values...

Euler sums | Multiple zeta values | Polygamma functions | Polylogarithm functions | Nonlinear Euler sums | Landen's identities | INTEGRALS | MATHEMATICS | nonlinear Euler sums | SERIES | multiple zeta values | RIEMANN ZETA-FUNCTION | STIRLING NUMBERS | VALUES | polygamma functions | polylogarithm functions

Euler sums | Multiple zeta values | Polygamma functions | Polylogarithm functions | Nonlinear Euler sums | Landen's identities | INTEGRALS | MATHEMATICS | nonlinear Euler sums | SERIES | multiple zeta values | RIEMANN ZETA-FUNCTION | STIRLING NUMBERS | VALUES | polygamma functions | polylogarithm functions

Journal Article

The Ramanujan Journal, ISSN 1382-4090, 10/2018, Volume 47, Issue 1, pp. 67 - 84

.... For a nonnegative integer k, we study the number $$N_f(D,k,b)$$ Nf(D,k,b) of k-subsets S in D such that $$\begin{aligned} \sum _{x\in S} f(x)=b. \end{aligned}$$ ∑x∈Sf(x)=b. In this paper, we establish several bounds for the difference...

Subset sum problem | Functions of a Complex Variable | Inclusion–exclusion | Field Theory and Polynomials | Character sums | Mathematics | Counting problems | 11T06 | Fourier Analysis | Number Theory | Combinatorics | 11T24 | 05A16 | Polynomial subset sums | 05A15 | EXPONENTIAL-SUMS | NUMBER | ALGEBRAIC-GEOMETRY CODES | FINITE-FIELDS | ENUMERATION | SUBGROUPS | POWERS | MATHEMATICS | PRIME-ORDER | PRODUCTS | BOUNDS | Inclusion-exclusion

Subset sum problem | Functions of a Complex Variable | Inclusion–exclusion | Field Theory and Polynomials | Character sums | Mathematics | Counting problems | 11T06 | Fourier Analysis | Number Theory | Combinatorics | 11T24 | 05A16 | Polynomial subset sums | 05A15 | EXPONENTIAL-SUMS | NUMBER | ALGEBRAIC-GEOMETRY CODES | FINITE-FIELDS | ENUMERATION | SUBGROUPS | POWERS | MATHEMATICS | PRIME-ORDER | PRODUCTS | BOUNDS | Inclusion-exclusion

Journal Article

1988, ISBN 0691084335, Volume no. 116., viii, 246

Book

Journal of Mathematical Physics, ISSN 0022-2488, 10/2011, Volume 52, Issue 10, pp. 102301 - 102301-52

The computation of Feynman integrals in massive higher order perturbative calculations in renormalizable quantum field theories requires extensions of multiply nested harmonic sums, which can be...

ANALYTIC CONTINUATION | polynomials | NUMERICAL EVALUATION | PHYSICS, MATHEMATICAL | ALGEBRAIC RELATIONS | HYPERGEOMETRIC-FUNCTIONS | integral equations | harmonics | perturbation theory | ONE-LOOP | renormalisation | MELLIN TRANSFORMS | LEGENDRE CHI | Feynman diagrams | MULTIPLE ZETA VALUES | NESTED SUMS

ANALYTIC CONTINUATION | polynomials | NUMERICAL EVALUATION | PHYSICS, MATHEMATICAL | ALGEBRAIC RELATIONS | HYPERGEOMETRIC-FUNCTIONS | integral equations | harmonics | perturbation theory | ONE-LOOP | renormalisation | MELLIN TRANSFORMS | LEGENDRE CHI | Feynman diagrams | MULTIPLE ZETA VALUES | NESTED SUMS

Journal Article

Mathematika, ISSN 0025-5793, 2019, Volume 65, Issue 3, pp. 437 - 474

We generalize the work of Sarnak and Tsimerman to twisted sums of Kloosterman sums and thus give evidence towards the twisted Linnik–Selberg conjecture.

11L05 (primary) | 11L07 | 11F72 (secondary) | FORMS | MATHEMATICS | COEFFICIENTS | MATHEMATICS, APPLIED

11L05 (primary) | 11L07 | 11F72 (secondary) | FORMS | MATHEMATICS | COEFFICIENTS | MATHEMATICS, APPLIED

Journal Article

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