List of Research Works*
Ekatherina Karatsuba

[44] E. A. Karatsuba, On one method for fast approximation of zeta constants by rational fractions, Problems of Information Transmission, volume 50, issue 2, pp. 186202 (2014). http://link.springer.com/article/10.1134%2FS0032946014020057 or http://dx.doi.org/10.1134/S0032946014020057

[43] E. A. Karatsuba, Fast Catalan constant computation via the approximations obtained by the Kummer's type transformations, Discrete Mathematics and Applications, volume 23, issues 5-6, pp. 429443 (2013).http://www.degruyter.com/view/j/dma.2013.23.issue-5-6/dma-2013-0029/dma-2013-0029.xml or http://dx.doi.org/10.1515/dma-2013-0029

[42] E. A. Karatsuba, On one asymptotic formula for the Euler constant // Problems of Information Transmission, Volume 48, Issue 4, pp. 342346 (2012).

[41] Anatolii A. Karatsuba and Ekatherina A. Karatsuba, Physical mathematics in number theory, Functional Analysis and Other Mathematics, Vol. 3, No. 2, 113-125 (2011).

[40] Anatolii A. Karatsuba and Ekatherina A. Karatsuba, On Application of the Functional Equation of the Jacobi Theta Function to Approximation of Atomic Inversion in the Jaynes-Cummings Model, Pacific Journal of Applied Mathematics, Vol. 2, No. 3, pp. 4163 (2010).

[39] Anatolii A Karatsuba, Ekatherina A. Karatsuba: Resummation formula for collapse and revival in the Jaynes-Cummings model, J. Phys. A: Math. Theor. 42, pp. 195304, 1--16 (2009).

[38] A. A. Karatsuba, E. A. Karatsuba. Application of ATS in a quantum-optical model. Analysis and Mathematical Physics: Trends in Mathematica Physics, Birkhauser Verlag, Basle, pp. 209--230 (2009).

[37] A. A. Karatsuba, E. A. Karatsuba. The "problem of remainders" in theoretical physics: "physical zeta" function. Proceedings of the 5th MATHEMATICAL PHYSICS MEETING: Summer School and Conference on Modern Mathematical Physics. Ed. by B. Dragovich and Z. Rakic. Institute of Physics, Belgrade, Serbia, pp. 197--210 (2009).

[36]E. A. Karatsuba. Zeros and points of discontinuity of the commutator function of the free Dirac field. Journal of Physics: Conference Series, IOP Publ., Vol.128, Quantum Information and Foundations of Quantum Theory, pp. 012015:1--11 (2008).

[35] Karatsuba E.A.: Investigating zeros and points of discontinuity of the commutator function of the free Dirac field. Abstracts "5th MATHEMATICAL PHYSICS MEETING: Summer School and Conference on Modern Mathematical Physics (Belgrade, Serbia, July 6--17, 2008)", p. 28 (2008).

[34]Karatsuba E.A.: The Commutator Function of the Free Dirac Field in the Discrete Representation and its Zeros. Pacific Journal of Applied Mathematics, Vol. 1, No. 2, pp. 37--55 (2008).

[33] Karatsuba E.A.: On an approach to the study of the JaynesCummings sum in quantum optics , J. of Numerical Algorithms,Proceedings of the First Dolomites workshop on constructive approximation theory and applications (DWCAA06) Vol. 45, No. 1-4 , pp. 127-137 (2007).

[32] Karatsuba E.A.: On approximation of exponential sums in certain physical problems. Abstracts "First Dolomites workshop on constructive approximation theory and applications (DWCAA06)", pp. 52-53 (2006).

[31] Karatsuba E.A.: Approximation of exponential sums in the problem on the oscillator motion caused by pushes (English). Chebyshev's transactions, Vol.6, No.3(15), pp.205-224 (2005).

[30] Karatsuba E.A., Moretti P.: Inversion time of large spins. (English) J. of Math. Phys., Vol.46, No.4, 042101-1—042101-7 (2005).

[29] Karatsuba E.A.: Approximation of sums of oscillating summands in certain physical problems. (English) J. of Math. Phys., Vol.45, No.11, pp.4310-4321 (2004).

[28] Karatsuba E.A.: On Some Problems of Approximation and Computation of Classical Functions and Constants. (Russian) Dissertation, Moscow, 136 pp., (2002).

[27] Karatsuba E.A.: On Some Problems of Approximation and Computation of Classical Functions and Constants. (Russian) Autoreferat of the dissertation, Moscow, 28 pp, (2002).

[26] Karatsuba E.A.: Fast computation of some special integrals of mathematical physics. (English) Scientific Computing, Validated Numerics, Interval Methods, W.Krämer, J.W.von Gudenberg, eds.; pp. 29-41, (2001).

[25] Karatsuba E.A.: Fast computation of  ζ(3)  and of some special integrals using the Ramanujan formula and polylogarithms. (English) BIT Numerical Mathematics, Vol.41, No.4, pp.722-730 (2001).

[24] Karatsuba E.A.: On the asymptotic representation of the Euler gamma function by Ramanujan. (English) J. Comput. Appl. Math. Vol.135, No.2, pp.225-240 (2001).

[23] Karatsuba E.A., Vuorinen M.: On hypergeometric functions and generalization of Legendre's relation. J. Math. Anal. Appl. Vol.260, No.2, pp.623-640 (2001).

[22] Karatsuba E.A.: On the computation of the Euler constant nbsp;γ.  (English) J. of Numerical Algorithms Vol.24, No.1-2, pp.83-97 (2000).

[21] Karatsuba E.A.: On the asymptotic representation of the Euler gamma function by Ramanujan. (English) University of Helsinki preprint, 22 pp. (1999).

[20] Karatsuba Ekatharine A.: Fast evaluation of hypergeometric function by FEE. (English) Papamichael, N. (ed.) et al., Proceedings of the 3rd CMFT conference on computational methods and function theory 1997, Nicosia, Cyprus, October 13-17, 1997. Singapore: World Scientific. Ser. Approx. Decompos. Vol.11, pp.303-314 (1999).

[19] Karatsuba E.A.: On the computation of the Euler constant gamma. University of Helsinki preprint, 21 pp. (1999).

[18] Karatsuba E.A., Vuorinen M.: On hypergeometric functions and generalization of Legendre's relation. University of Helsinki preprint, 16 pp. (1998).

[17] Karatsuba E.A.: Fast evaluation of the Hurwitz zeta Function and Dirichlet L-series. (Russian, English) Probl. Inf. Transm. Vol.34, No.4, pp.342-353 (1998); translation from Probl. Peredachi. Inf. Vol.34, No.4, pp.62-75 (1998).

[16] Karatsuba Ekaterina A.: New correlations between the Riemann zeta function and the derivatives of the gamma function and their application to fast computation of the Riemann zeta function. (English) 4-th Symposium on Mathematical Analysis and Its Applications, Abstracts, Beograd, pp.63-64, (1997).

[15] Karatsuba E.A.: Fast computation of the Riemann zeta function for integer argument. (Russian, English) Dokl. Math. Vol.54, No.1, p.626 (1996); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk Vol.349, No.4, p.463 (1996).

[14] Karatsuba E.A.: Fast computation of the Riemann zeta-function  ζ(s)  for integer values of the argument s. (Russian, English) Probl. Inf. Transm. Vol.31, No.4, pp.353-362 (1995); translation from Probl. Peredachi Inf. Vol. 31, No.4, pp.69-80 (1995).

[13] Karatsuba E.A.: On the FEE-Method  Method for Fast Evaluating the Functions Like E-Functions. (English) Abstracts of the International Conference "Symbolic Calculations and Their Application in Fundamental Reseachers", ITA RAS, St.Petersburg, p.26, (1995).

[12] Karatsuba E.A.: The Method FEE, Lectures of the second International conference "Mathematical Algorithms". (Russian) Niznij Novgorod, (1995).

[11] Karatsuba Catherine A.: Fast Evaluation of Bessel Functions. (English) Integral Transforms and Spec. Funct. Vol.1, No.4, pp.269-276 (1993).

[10] Karatsuba E.A.: Fast evaluation of  ζ(3).  (Russian, English) Probl. Inf. Transm. Vol.29, No.1, pp.58-62 (1993); translation from Probl. Peredachi Inf. Vol.29, No.1, pp.68-73 (1993).

[9] Karatsuba E.A.: Fast computation of the number  ζ(3),  ( ζ(s)  Riemann zeta-function). (Russian) Probl. Peredachi Informat., Vol.28, No.3, p.112, Chronicle. 19-th Russian School on Theory of Information and its Applications, (1992).

[8] Karatsuba E.A.: The complexity of calculation of Transcendental Functions. (Russian) Lectures of the 3-d All-Union Conference on SuperComputers, Moscow, (1992).

[7] Karatsuba E.A.: The estimation of the efficacy of fast algorithms for computations of some classes of transcendental functions. (Russian) Dissertation, Moscow, 95 pp., (1991).

[6] Karatsuba E.A.: The estimation of the efficacy of fast algorithms for computations of some classes of transcendental functions. (Russian) Autoreferat of the dissertation, Moscow, 10 pp., (1991).

[5] Karatsuba E.A.: Fast evaluation of transcendental functions. (Russian, English) Probl. Inf. Transm. Vol.27, No.4, pp.339-360 (1991); translation from Probl. Peredachi Inf. Vol.27, No.4, pp.87-110 (1991).

[4] Karatsuba E.A.: On fast computation of transcendental functions. (Russian, English) Sov. Math., Dokl. Vol.43, No.3, pp.693-694 (1991); translation from Dokl. Akad. Nauk SSSR Vol.318, No.2, pp.278-279 (1991).

[3] Karatsuba E.A.: On a new method for fast evaluation of transcendental functions. (Russian, English) Russ. Math. Surv. Vol.46, No.2, pp.246-247 (1991); translation from Usp. Mat. Nauk Vol.46, No.2(278), pp.219-220 (1991).

[2] Karatsuba E.A.: Fast computation of exp(x). (Russian) Problems of Information Transmission, Vol. 26, No.3, p.109, Chronicle-17th All-Union School on Theory of Information and its Applications, (1990).

[1] Karatsuba E.A.: Arithmetic-geometrical mean (AGM) methods for fast evaluations the constants like  π.  (Russian) Probl. of Informat. Transmis., Vol. 25, No.3, p.11, Cronicle-16th All-Union School on Theory of Information and its Applications, (1989).

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© Ekatherina Karatsuba
Last correction: September 16, 2014.