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SIAM journal on optimization, ISSN 1095-7189, 2019, Volume 29, Issue 2, pp. 1106 - 1130
.... The main contribution of this paper consists of providing formulas for such a subdifferential under weak continuity assumptions... 
MATHEMATICS, APPLIED | CONVEX | convex functions | CONSTRAINT QUALIFICATIONS | qualification conditions | subdifferential calculus rules | CALCULUS RULES | SUM | supremum function | OPTIMALITY CONDITIONS | SEMIINFINITE
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 4/2019, Volume 291, Issue 3, pp. 1337 - 1356
We prove a weighted sum formula of the zeta values at even arguments, and a weighted sum formula of the multiple zeta values with even arguments and its zeta-star analogue... 
Weighted sum formulas | Bernoulli numbers | 11M32 | Multiple zeta values | Mathematics, general | Mathematics | Multiple zeta-star values | 11B68 | MATHEMATICS
Journal Article
Inventiones mathematicae, ISSN 0020-9910, 12/2013, Volume 194, Issue 3, pp. 673 - 729
Journal Article
Journal of Number Theory, ISSN 0022-314X, 05/2016, Volume 162, pp. 483 - 495
We discover new Voronoi formulae for automorphic forms on GL(n) for n≥4. There are [n/2] different Voronoi formulae on GL... 
Kloosterman sum | Maass form | Voronoi formula | Automorphic form | Functional equation | MATHEMATICS | Mathematics - Number Theory
Journal Article
Odontology, ISSN 1618-1247, 2019, Volume 107, Issue 1, pp. 72 - 79
...) formulas and the gingival color space using the Bland and Altman limits of agreement, to use this relationship to establish the equivalences between the gingival color thresholds of perceptibility... 
CIEDE2000 formula | CIELAB formula | Dentistry | Oral and Maxillofacial Surgery | Gingiva color measurement | Bland and Altman limits of agreement | Bland and Altman limits ofagreement | agreement | ZIRCONIA | PERFORMANCE | SOFT-TISSUE | RESTORATIONS | MUCOSA | DENTISTRY, ORAL SURGERY & MEDICINE | IMPLANT ABUTMENTS | CIELAB | Bland and Altman limits of | DELTA-E-ASTERISK | STANDARDIZED RESIDUAL SUM | SHADE GUIDE | Confidence intervals | Transformation | Gingiva | Color
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 1/2016, Volume 39, Issue 1, pp. 31 - 47
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 03/2016, Volume 12, Issue 2, pp. 383 - 408
In this paper, explicit formulas involving a generalized Ramanujan sum are derived... 
Ramanujan sums | prime number theorem | explicit formulas | MATHEMATICS | MOBIUS FUNCTION
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 1/2018, Volume 45, Issue 1, pp. 73 - 94
In terms of Abel’s transformation on difference operators, we establish four families of summation formulas involving generalized harmonic numbers... 
Fourier Analysis | Secondary 40A25 | Functions of a Complex Variable | Difference operator | Harmonic numbers | Field Theory and Polynomials | Primary 05A19 | Abel’s transformation | Mathematics | Number Theory | Combinatorics | MATHEMATICS | IDENTITIES | Abel's transformation | SUMS
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2016, Volume 2016, Issue 1, pp. 1 - 7
In this paper we present two computational formulae for one kind of reciprocal sums related to the Riemann zeta-function at integer points s = 4 , 5 $s=4,5... 
inequality | telescoping method | continued fraction | 11B83 | Analysis | multiple-correction method | Mathematics, general | Mathematics | 11M06 | 11J70 | Applications of Mathematics | Riemann zeta-function | PELL | MATHEMATICS | MATHEMATICS, APPLIED | RECIPROCAL FIBONACCI | FIBONACCI POLYNOMIALS | MULTIPLE-CORRECTION | INFINITE SUM | Integers | Texts | Computation | Inequalities | Sums
Journal Article
Taiwanese journal of mathematics, ISSN 1027-5487, 4/2016, Volume 20, Issue 2, pp. 243 - 261
In this paper, we introduce the vectorization of shuffle products of two sums of multiple zeta values, which generalizes the weighted sum formula obtained by Ohno and Zudilin... 
Integers | Mathematics | Weighted sum formula | Multiple zeta value | Shuffle relation | Sum formula | MATHEMATICS
Journal Article
Journal of Algebraic Combinatorics, ISSN 0925-9899, 8/2019, Volume 50, Issue 1, pp. 73 - 98
.... Closed formulas for exponential sums of symmetric Boolean functions were found by Cai, Green and Thierauf in the late 1990s... 
Convex and Discrete Geometry | Symmetric functions | 05E05 | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Linear recurrences | Combinatorics | Computer Science, general | Exponential sums | 11T23 | 11B37 | MATHEMATICS | PERTURBATIONS | Cryptography
Journal Article
Frontiers of Mathematics in China, ISSN 1673-3452, 2/2014, Volume 9, Issue 1, pp. 101 - 109
...Front. Math. China 2014, 9(1): 101–109 DOI 10.1007/s11464-013-0348-0 Multiplication formulas for Kubert functions Hailong LI 1 , Jing MA 2 , Yuichi URAMATSU 3... 
multiplication formula | integral formula | Mathematics, general | Kubert function | Mathematics | Bernoulli polynomial | mean value | 11A25 | 11B68 | MATHEMATICS | DEDEKIND SUMS | IDENTITIES | HECKE OPERATORS | HURWITZ ZETA-FUNCTION | Studies | Polynomials | Multiplication & division | Integrals | Mathematical analysis | Dirichlet problem
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2012, Volume 262, Issue 4, pp. 1515 - 1528
Let X and Y be two n × n Hermitian matrices. In the article Proof of a conjectured exponential formula... 
Functional calculus | Operator identity | Unitary operators | MATHEMATICS | EIGENVALUES | INEQUALITIES | HONEYCOMB MODEL | HERMITIAN MATRICES | CONJECTURE | SUMS
Journal Article
Mathematica Slovaca, ISSN 0139-9918, 8/2013, Volume 63, Issue 4, pp. 733 - 758
... ). And we obtain four infinite families of recursive formulas for the power moments of Kloosterman sums and four those of 2-dimensional Kloosterman sums in terms of the frequencies of weights in the codes... 
special orthogonal group | Kloosterman sum | Algebra | weight distribution | Mathematics, general | Primary 11T23, 20G40, 94B05 | Mathematics | 2-dimensional Kloosterman sum | double cosets | Pless power moment identity | maximal parabolic subgroup | orthogonal group | MATHEMATICS | CODES | FINITE-FIELD | SYMPLECTIC GROUPS | GAUSS SUMS
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 2/2019, Volume 48, Issue 2, pp. 323 - 349
In this paper, transformation formulas for the function $$\begin{aligned} A_{1}\left( z,s:\chi \right) =\sum \limits _{n=1}^{\infty }\sum \limits _{m=1... 
Bernoulli and Euler polynomials | Fourier Analysis | Functions of a Complex Variable | Hardy–Berndt sums | Dedekind sums | Field Theory and Polynomials | Mathematics | Number Theory | Combinatorics | 11F20 | 11B68
Journal Article
Annals of the Institute of Statistical Mathematics, ISSN 0020-3157, 10/2014, Volume 66, Issue 5, pp. 833 - 864
Journal Article
Applied mathematics and computation, ISSN 0096-3003, 10/2020, Volume 383, p. 125380
•We provide an asymptotic formula for Vasyunin cotangent sums.•Vasyunin cotangent sums have applications in Riemann Hypothesis... 
Vasyunin cotangent sums | Euler-Maclaurin summation formula | Digamma function | MATHEMATICS, APPLIED
Journal Article
Journal of Siberian Federal University - Mathematics and Physics, ISSN 1997-1397, 2018, Volume 11, Issue 5, pp. 603 - 614
... Arising From Collection Formulas Vladimir M. Leontiev∗ Institute of Mathematics and Computer Science Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041... 
Sums of binomial coefficients | Divisibility | Collection formulas
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 12/2017, Volume 488, pp. 46 - 55
Journal Article
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