International Journal of Number Theory, ISSN 1793-0421, 11/2018, Volume 14, Issue 10, pp. 2617 - 2630

For positive integers m , n , k with m ≥ 2 and ⌈ n / 2 ⌉ ≤ k ≤ n , let E { m } ( m , n , k ) be the sum of multiple zeta values of depth k and weight m n with...

modified Bell polynomial | generating function | stuffle relation | Multiple zeta value | MATHEMATICS | SERIES | stale relation

modified Bell polynomial | generating function | stuffle relation | Multiple zeta value | MATHEMATICS | SERIES | stale relation

Journal Article

1984, ISBN 9780821823057, Volume no. 304., vi, 184

Book

International Journal of Number Theory, ISSN 1793-0421, 10/2017, Volume 13, Issue 9, pp. 2253 - 2264

For a real number β ≠ 0 and positive integers m and n with m ≥ 2 , we evaluate the sum of multiple zeta values ∑ k = 1 n ∑ | α | = n β α 1 β α 2 ⋯ β α k ζ ( m...

MATHEMATICS | multiple zeta-star value | digamma function | Multiple zeta value | gamma function

MATHEMATICS | multiple zeta-star value | digamma function | Multiple zeta value | gamma function

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 02/2016, Volume 12, Issue 1, pp. 15 - 25

In this paper, we extend the Euler decomposition theorem to a much more general form of the decomposition of the product of n multiple zeta values of height...

Multiple zeta value | Euler decomposition theorem | MATHEMATICS | SUM FORMULA

Multiple zeta value | Euler decomposition theorem | MATHEMATICS | SUM FORMULA

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 08/2013, Volume 9, Issue 5, pp. 1185 - 1198

In this paper, we compute shuffle relations from multiple zeta values of the form ζ({1}m-1, n+1) or sums of multiple zeta values of fixed weight and depth....

weighted sum formula | shuffle relation | sum formula | Multiple zeta value | MATHEMATICS | HARMONIC SERIES

weighted sum formula | shuffle relation | sum formula | Multiple zeta value | MATHEMATICS | HARMONIC SERIES

Journal Article

Functiones et Approximatio, Commentarii Mathematici, ISSN 0208-6573, 2012, Volume 46, Issue 1, pp. 63 - 77

For positive integers \alpha_{1}, \alpha_{2}, \ldots, \alpha_{r} with \alpha_{r} \geq 2, the multiple zeta value or r-fold Euler sum is defined by...

Euler sums | Stuffle formulae | Multiple zeta value | Hurwitz zeta function | 33E99 | 11M99 | stuffle formulae | 40B05 | multiple zeta value | 40A25

Euler sums | Stuffle formulae | Multiple zeta value | Hurwitz zeta function | 33E99 | 11M99 | stuffle formulae | 40B05 | multiple zeta value | 40A25

Journal Article

Journal of Number Theory, ISSN 0022-314X, 05/2015, Volume 150, pp. 1 - 20

The classical Euler decomposition theorem expresses a product of two Riemann zeta values in terms of double Euler sums. Also, the sum formula expresses a...

Multiple zeta value | Euler decomposition theorem | MATHEMATICS

Multiple zeta value | Euler decomposition theorem | MATHEMATICS

Journal Article

Journal of number theory, ISSN 0022-314X, 2009, Volume 129, Issue 4, pp. 908 - 921

For positive integers α 1 , α 2 , … , α r with α r ⩾ 2 , the multiple zeta value or r-fold Euler sum is defined as ζ ( α ) : = ζ ( α 1 , α 2 , … , α r ) = ∑ 1...

Drinfeld integral | Multiple zeta value | Sum formula | MATHEMATICS | HARMONIC SERIES | EULER SUMS | EXPLICIT EVALUATION

Drinfeld integral | Multiple zeta value | Sum formula | MATHEMATICS | HARMONIC SERIES | EULER SUMS | EXPLICIT EVALUATION

Journal Article

The Rocky Mountain journal of mathematics, ISSN 0035-7596, 04/2020, Volume 50, Issue 2, pp. 551 - 558

We evaluate the multiple zeta value zeta(1, {2}(n+1)) or its dual zeta({2}(n),( )3). When n is even, along with stuffle relations already available, it is...

modified Bell polynomial | MATHEMATICS | multiple zeta-star value | multiple zeta value | Bernoulli polynomial

modified Bell polynomial | MATHEMATICS | multiple zeta-star value | multiple zeta value | Bernoulli polynomial

Journal Article

Journal of Number Theory, ISSN 0022-314X, 07/2018, Volume 188, pp. 247 - 262

In this paper, we are going to evaluate a family {Ep(2m,n,k)|p∈Z} of sums of multiple zeta values with even arguments and polynomial weights defined...

Multiple zeta values | Weighted sum formula | Multiple zeta-star value | MATHEMATICS

Multiple zeta values | Weighted sum formula | Multiple zeta-star value | MATHEMATICS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 03/1996, Volume 348, Issue 3, pp. 1117 - 1136

Generalized Bernoulli polynomials were introduced by Shintani in 1976 in order to express the special values at non-positive integers of Dedekind zeta...

Integers | Numbers | Series convergence | Analytic functions | Real numbers | Paper | Polynomials | Mathematical functions | Coefficients | Vertices | MATHEMATICS

Integers | Numbers | Series convergence | Analytic functions | Real numbers | Paper | Polynomials | Mathematical functions | Coefficients | Vertices | MATHEMATICS

Journal Article

Journal of Number Theory, ISSN 0022-314X, 2006, Volume 117, Issue 1, pp. 31 - 52

In this paper, we consider two types of extended Euler sums: E p , q ( k ) = ∑ n = 1 ∞ 1 n q ∑ r = 1 kn 1 r p , T p , q ( k ) = ∑ n = 1 ∞ 1 n q ∑ r = 1 ⌊ n / k...

Zeta function | Euler sum | Bernoulli polynomial | POLYNOMIALS | MATHEMATICS | zeta function | INTEGRAL-REPRESENTATIONS | Computer science

Zeta function | Euler sum | Bernoulli polynomial | POLYNOMIALS | MATHEMATICS | zeta function | INTEGRAL-REPRESENTATIONS | Computer science

Journal Article

10/2018

In this paper, we investigate the Euler sums $$ G_{n+2}(p,q)=\sum_{1\leq k_1 Mathematics - Number Theory

Journal Article

15.
Full Text
Sum formulas of multiple zeta values with arguments multiples of a common positive integer

Journal of Number Theory, ISSN 0022-314X, 08/2017, Volume 177, pp. 479 - 496

For k≤n, let E(m,n,k) be the sum of all multiple zeta values of depth k and weight mn with arguments multiples of m≥2. More precisely,...

Multiple zeta values | Multiple zeta-star values | MATHEMATICS

Multiple zeta values | Multiple zeta-star values | MATHEMATICS

Journal Article

Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 2017, Volume 47, Issue 7, pp. 2107 - 2131

In this paper, we build some variations of multiple zeta values and investigate their relations. Among other things, we prove that Sigma(|alpha| = m+r 1 <= k1...

Restricted sum formula | Duality theorem | Multiple zeta value | Sum formula | MATHEMATICS | restricted sum formula | sum formula | duality theorem

Restricted sum formula | Duality theorem | Multiple zeta value | Sum formula | MATHEMATICS | restricted sum formula | sum formula | duality theorem

Journal Article

International Journal of Number Theory, ISSN 1793-0421, 06/2008, Volume 4, Issue 3, pp. 437 - 451

The triple Euler sum defined by \[ \begin{array}{rcl} \zeta(p, q, r) & = & \sum\limits_{\ell=3}^{\infty} \frac{1}{\ell^{p}} \sum\limits_{k=2}^{\ell-1}...

MATHEMATICS | triple Euler sums | Hurwitz zeta function

MATHEMATICS | triple Euler sums | Hurwitz zeta function

Journal Article

Journal of Number Theory, ISSN 0022-314X, 07/2016, Volume 164, pp. 208 - 222

The duality theorem and sum formula [8] are undoubtedly the crucial relations among multiple zeta values. They can be expressed as ζ({1}p,q+2)=ζ({1}q,p+2)...

Multiple zeta values | Drinfel'd integrals | Sum formula | Secondary | Primary | MATHEMATICS

Multiple zeta values | Drinfel'd integrals | Sum formula | Secondary | Primary | MATHEMATICS

Journal Article

Revista Matematica Iberoamericana, ISSN 0213-2230, 2000, Volume 16, Issue 3, pp. 571 - 596

We shall develop the general theory of Jacobi forms of degree two over Cayley numbers and then construct a family of Jacobi-Eisenstein series which forms the...

FORMS | MATHEMATICS | MAASS SPACE

FORMS | MATHEMATICS | MAASS SPACE

Journal Article

Journal of Number Theory, ISSN 0022-314X, 08/2013, Volume 133, Issue 8, pp. 2475 - 2495

The classical Euler decomposition theorem expressed a product of two Riemann zeta values in terms of double Euler sums. Such kind of decomposition theorem are...

Euler sums | Multiple zeta values | Euler decomposition theorem | Shuffle product formula | Drinfeld integrals | MATHEMATICS | VALUES | SUM FORMULA

Euler sums | Multiple zeta values | Euler decomposition theorem | Shuffle product formula | Drinfeld integrals | MATHEMATICS | VALUES | SUM FORMULA

Journal Article

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