Papers / Articles
In Journals
- (with H. Maier) Cotangent sums related to the Riemann Hypothesis for various shifts of the argument, preprint.
- (with H. Maier) Distribution of a cotangent sum related to the Nyman-Beurling criterion for the Riemann Hypothesis, Applied Mathematics and Computation, 363(15)(2019), https://doi.org/10.1016/j.amc.2019.124589.
- Vijay Gupta, Deepika Agrawal and Michael Th. Rassias, Quantitative Estimates for Differences of Baskakov-type Operators, Complex Analysis and Operator Theory (to appear).
- Michael Th. Rassias, Bicheng Yang and Andrei Raigorodskii, On the Reverse Hardy -Type Integral Inequalities in the Whole Plane with the Extended Riemann-Zeta Function, Journal of Mathematical Inequalities (to appear).
- (with C. Park) Additive functional equations and partial multipliers in C*-algebras, Revista de la Real Academia de Ciencias Exactas, Serie A. Matemáticas, 113(3)(2019), 2261-2275.
- (with H. Maier) Explicit estimates of sums related to the Nyman-Beurling criterion for the Riemann Hypothesis, Journal of Functional Analysis, 276(2019), 3832-3857.
- (with B. Yang) On an Equivalent Property of a Reverse Hilbert-Type Integral Inequality Related to the Extended Hurwitz-Zeta Function, Journal of Mathematical Inequalities, 13(2)(2019), 315-334.
- (with B. Yang) On a Hilbert-type integral inequality in the whole plane related to the extended Riemann zeta function, Complex Analysis and Operator Theory, 13(4)(2019), 1765-1782.
- (with B. Yang) A reverse Mulholland-type inequality in the whole plane with multi-parameters, Applicable Analysis and Discrete Mathematics, 13(1)(2019), 290-308.
- (with M. R. Abdollahpour) Hyers-Ulam stability of hypergeometric differential equations, Aequationes Mathematicae, (93)(4)(2019), 691-698.
- (with B. Yang) On a Hilbert-type integral inequality related to the extended Hurwitz zeta function in the whole plane, Acta Applicandae Mathematicae, 160(1)(2019), 67-80.
- (with H. Maier) On the size of an expression in the Nyman-Beurling-Baez-Duarte criterion for the Riemann Hypothesis, Canadian Mathematical Bulletin, 61(3)(2018), 622-627.
- (with B. Yang and A. Raigorodskii), Two Kinds of the Reverse Hardy-Type Integral Inequalities with the Equivalent Forms Related to the Extended Riemann Zeta Function, Applicable Analysis and Discrete Mathematics, 12(2018), 273–296.
- (with B. Yang) Equivalent properties of a Hilbert-type integral inequality with the best constant factor related to the Hurwitz zeta function, Annals of Functional Analysis, 9(2)(2018), 282-295.
- (with H. Maier) Estimates of sums related to the Nyman-Beurling criterion for the Riemann Hypothesis, Journal of Number Theory, 188(2018), 96–120.
- (with H. Maier) Asymptotics for moments of certain cotangent sums for arbitrary exponents, Houston Journal of Mathematics, 43(4)(2017), 1235–1249.
- (with Y. -H. Lee and S. -M. Jung) Uniqueness theorems on functional inequalities concerning cubic-quadratic-additive equation, Journal of Mathematical Inequalities, 12(1)(2018), 43–61.
- (with B. Yang) A half-discrete Hilbert-type inequality in the whole plane related to the Riemann zeta function, Applicable Analysis, 97(9)(2018), 1505-1525.
- From a cotangent sum to a generalized totient function, Applicable Analysis and Discrete Mathematics, 11(2017), 369–385.
- (with H. Maier) The maximum of cotangent sums related to Estermann's zeta function in rational numbers in short intervals, Applicable Analysis and Discrete Mathematics, 11(2017), 166–176.
- (with H. Maier) Asymptotics for moments of certain cotangent sums, Houston Journal of Mathematics, 43(1)(2017), 207-222.
- (with B. Yang) Equivalent conditions of a Hardy-type integral inequality related to the extended Riemann zeta function, Advances in Operator Theory, 2(3)(2017), 237- 256.
- (with H. Maier) Large gaps between consecutive prime numbers containing perfect k-th powers of prime numbers, Journal of Functional Analysis, 272(2017) 2659-2696.
- (with H. Maier) The ternary Goldbach problem with a prime and two isolated primes, Proceedings of the Steklov Institute of Mathematics, 296(2017), 183-197. Also translated in Russian and published in Trudy Matematich. Instituta im. V.A. Steklova, 296(2017), 192-206.
- (with H. Maier) Generalizations of a cotangent sum associated to the Estermann zeta function, Communications in Contemporary Mathematics, 18(1)(2016), 89 pages, DOI: 10.1142/S0219199715500789.
- (with M. R. Abdollahpour and R. Aghayaria) Hyers-Ulam stability of associated Laguerre differential equations in a subclass of analytic functions, Journal of Mathematical Analysis and Applications, 437(2016), 605- 612.
- (with H. Maier) The rate of growth of moments of certain cotangent sums, Aequationes Mathematicae, 90(3)(2016), 581- 595.
- (with H. Maier) Large gaps between consecutive prime numbers containing square-free numbers and perfect powers of prime numbers, Proceedings of the American Mathematical Society, 144(2016), 3347 - 3354.
- (with B. Yang) On a Hardy-Hilbert-type inequality with a general homogeneous kernel, International Journal of Nonlinear Analysis and Applications, 7(1)(2016), 249-269.
- (with H. Maier) The order of magnitude for moments for certain cotangent sums, Journal of Mathematical Analysis and Applications, 429(1)(2015), 576-590.
- (with B. Yang) A Hilbert-type integral inequality in the whole plane related to the hypergeometric function and the Beta function, Journal of Mathematical Analysis and Applications, 428(2)(2015), 1286-1308.
- (with S. -M. Jung and C. Mortici) On a functional equation of trigonometric type, Applied Mathematics and Computation, 252(2015), 294-303.
- (with C. Mortici) On the growth rate of divergent series, Journal of Number Theory, 147(2015), 499–507.
- On the representation of the number of integral points of an elliptic curve modulo a prime number, The Ramanujan Journal, Springer, 36(3)(2015), 483–499.
- (with B. Yang) On a multidimensional Hilbert-type integral inequality associated to the Gamma function, Applied Mathematics and Computation, 249(2014), 408-418.
- (with C. Mortici and S. -M. Jung) On the stability of a functional equation associated with the Fibonacci numbers, Abstract and Applied Analysis, Volume 2014 (2014), Article ID 546046, 6 pages.
- (with B. Yang) On a multidimensional half-discrete Hilbert-type inequality related to the hyperbolic cotangent function, Applied Mathematics and Computation, 242(2014), 800–813.
- (with S. -M. Jung) A linear functional equation of third order associated to the Fibonacci numbers, Abstract and Applied Analysis, Volume 2014 (2014), Article ID 137468, 7 pages.
- A cotangent sum related to zeros of the Estermann zeta function, Applied Mathematics and Computation, 240(2014), 161–167.
- (with S. -M. Jung and D. Popa) On the stability of the linear functional equation in a single variable on complete metric groups, Journal of Global Optimization, 59(2014), 165–171.
- (with Y. -H. Lee and S. -M. Jung) On an n-dimensional mixed type additive and quadratic functional equation, Applied Mathematics and Computation, 228(2014), 13–16.
- (with B. Yang) A multidimensional half-discrete Hilbert-type inequality and the Riemann zeta function, Applied Mathematics and Computation, 225(2013), 263–277.
- (with B. Yang) On half-discrete Hilbert’s inequality, Applied Mathematics and Computation, 220(2013), 75–93.
- (with G. V. Milovanović) Some properties of a hypergeometric function which appear in an approximation problem, Journal of Global Optimization, 57(2013), 1173–1192.
- (with P. Mihăilescu) Public key cryptography, number theory and applications, Newsletter, European Mathematical Society, 86(2012), 25–30.
In collected volumes
- (with B. Yang) A half-discrete Hardy-Hilbert-type inequality with a best possible constant factor related to the Hurwitz zeta function, In: Progress in Approximation Theory and Applicable Complex Analysis: In the Memory of Q. I. Rahman, Springer, 2017, 183-218.
- (with H. Maier) Asymptotics and equidistribution of cotangent sums associated to the Estermann and Riemann zeta functions, In: From Arithmetic to Zeta-Functions. Number Theory in Memory of Wolfgang Schwarz, Springer, Basel, 2016, 277-293.
- (with L. Tóth) Trigonometric representations of generalized Dedekind and Hardy sums via the discrete Fourier transform, In: Analytic Number Theory. In honor of Helmut Maier's 60th birthday, Springer, New York, 2015, 329-343.
- (with B. Tams and P. Mihăilescu) Current challenges for IT security with focus on Biometry, In: Computation, Cryptography, and Network Security, Springer, New York, 2015, 461-491.
- (with B. Yang) Parameterized Yang-Hilbert-type integral inequalities and their operator expressions, In: Computation, Cryptography, and Network Security, Springer, New York, 2015, 635-736.
- (with B. Yang) A multidimensional Hilbert-type integral inequality related to the Riemann zeta function, In: Applications of Mathematics and Informatics in Science and Engineering, Springer, New York, 2014, 417–433.
- (with P. Mihăilescu) Computational number theory and cryptography, In: Applications of Mathematics and Informatics in Science and Engineering, Springer, New York, 2014, 349–373.