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Inventiones mathematicae, ISSN 0020-9910, 12/2013, Volume 194, Issue 3, pp. 673 - 729
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 1/2016, Volume 39, Issue 1, pp. 31 - 47
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
Annals of the Institute of Statistical Mathematics, ISSN 0020-3157, 10/2014, Volume 66, Issue 5, pp. 833 - 864
Journal Article
Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2015, Volume 67, Issue 3, pp. 1069 - 1076
Journal Article
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
International Journal of Number Theory, ISSN 1793-0421, 08/2019, Volume 15, Issue 7, pp. 1469 - 1472
Let s ( a , b ) denote the classical Dedekind sum and S ( a , b ) = 1 2 s ( a , b ) . Recently, Du and Zhang proved the following reciprocity formula... 
MATHEMATICS | Dedekind sums | reciprocity laws for Dedekind sums
Journal Article
Optics Express, ISSN 1094-4087, 02/2014, Volume 22, Issue 3, pp. 3458 - 3467
.... Using the Standardized Residual Sum of Squares (STRESS) index, the results of our visual experiment were tested against predictions made by 12 modern color-difference formulas... 
STANDARDIZED RESIDUAL SUM | OPTICS | Image Processing | Computer Science
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
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
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 06/2011, Volume 44, Issue 22, pp. 225302 - 11
We present a short alternative proof of the Voronoi summation formula which plays an important role in Dirichlet's divisor problem and has recently found an application in physics as a trace formula... 
EXPONENTIAL-SUMS | PHYSICS, MULTIDISCIPLINARY | STRONGLY CHAOTIC SYSTEMS | RIEMANN ZETA-FUNCTION | PERIODIC-ORBIT THEORY | PHYSICS, MATHEMATICAL | SPECTRAL STATISTICS | QUANTUM GRAPHS | Dirichlet problem | Graphs | Operators | Schroedinger equation | Mathematical analysis | Proving
Journal Article
American journal of mathematics, ISSN 0002-9327, 4/2008, Volume 130, Issue 2, pp. 359 - 383
We give a combinatorial formula for the nonsymmetric Macdonald polynomials Eµ(x; q, t). The formula generalizes our previous combinatorial interpretation of the integral form symmetric Macdonald polynomials... 
Research fellowships | Algebra | Root systems | Partial sums | Polynomials | Mathematical functions | Combinatorics | Coefficients | Symmetry | MATHEMATICS | Mathematics | Formulae | Properties | Geometry | Theorems | Numerical analysis
Journal Article
Advances in Difference Equations, ISSN 1687-1839, 12/2017, Volume 2017, Issue 1, pp. 1 - 5
We give two extensions of the classical formula for sums of powers on arithmetic progressions... 
binomial transform | Bernoulli polynomials | forward difference | sum of powers formula | binomial mixture | MATHEMATICS | MATHEMATICS, APPLIED | OPERATORS | Usage | Binomial theorem | Polynomials | Progressions | Sums | Arithmetic
Journal Article
Bulletin of the Korean Mathematical Society, ISSN 1015-8634, 2016, Volume 53, Issue 2, pp. 487 - 494
... the computational problem of one kind mean value function related to E(c, p) = N(c, p) - 1/2 phi(p), and give its an exact computational formula. 
Computational formula | Mean value | Error term | Lehmer’s problem | MATHEMATICS | error term | mean value | DEDEKIND SUMS | Lehmer's problem | computational formula
Journal Article
Physics Letters A, ISSN 0375-9601, 10/2011, Volume 375, Issue 42, pp. 3659 - 3663
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 08/2014, Volume 10, Issue 5, pp. 1099 - 1119
Ramanujan's formula for the number r24(n) of representations of a positive integer n as a sum of 24 squares asserts that \begin{eqnarray*} r_{24}(n) & = & \frac... 
sums of squares and triangular numbers | modular forms | Ramanujan's tau function | sum of divisors function | Eisenstein series | infinite products | Dedekind eta function | Ramanujan's 24 squares formula | MATHEMATICS | Heterocyclic compounds
Journal Article
International Journal of Number Theory, ISSN 1793-0421, 12/2016, Volume 12, Issue 8, pp. 2061 - 2072
Dedekind used the classical Dedekind sum D ( a , c ) to describe the transformation of log η ( z ) under the substitution z ′ = ( a z + b ) / ( c z + d ) , ( a... 
Dedekind sum | function fields | Dedekind eta function | MATHEMATICS
Journal Article
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