transcendental number, independence and irrationality of numbers, measures of irrationality and transcendence, Riemann zeta function.
Коды УДК:
511.3
Основные темы научной работы
Number theory in general, diophantine equations, diophantine approximations;
Transcendental number theory, linear independence and irrationality of numbers;
Measures of irrationality and transcendence, hypergeometric functions;
Polylogarithmic functions, Riemann zeta function, multiple zeta values;
Pade approximations, number-theoretic remarkable constants;
General topology.
Основные публикации:
Kh. Hessami Pilehrood, T. Hessami Pilehrood. Generating function identities for $\zeta(2n+2),\zeta(2n+3)$ via the WZ method, submitted for publication.
Kh. Hessami Pilehrood, T. Hessami Pilehrood. Approximations to Euler's constant, submitted for publication. arXiv:0708.2771 [math.NT].
Kh. Hessami Pilehrood, T. Hessami Pilehrood. On transcendence of certain infinite series, submitted for publication.
Kh. Hessami Pilehrood, T. Hessami Pilehrood. Apery-like recursion and continued fraction for $\pi\coth\pi$, submitted for publication.
Kh. Hessami Pilehrood, T. Hessami Pilehrood. On a conjecture of Erdos, accepted for publication, to appear in Math. Notes.
Kh. Hessami Pilehrood, T. Hessami Pilehrood.Infinite sums as linear combinations of polygamma functions, accepted for publication, to appear in Acta Arithmetica.
Kh. Hessami Pilehrood, T. Hessami Pilehrood. On conditional irrationality measures for the values of digamma function, J. Number Theory, 123 (2007), no. 1, p. 241–253.
Kh. Hessami Pilehrood, T. Hessami Pilehrood. Arithmetical properties of some series with logarithmic coefficients, Math. Zeitschrift, 255 (2007), no. 1, p. 117–131.
Kh. Hessami Pilehrood, T. Hessami Pilehrood, W. Zudilin. Irrationality of certain numbers that contain values of the di- and trilogarithmhttp, Math. Zeitschrift, 254 (2006), no. 2, p. 299–313.
T. Hessami Pilehrood, Kh. Hessami Pilehrood. On irrationality of sums of zeta values, Mat. Zametki, 79 (2006), no. 4, p. 607–618; English transl.: Math. Notes, 79 (2006), no. 4, p. 561–571.
Kh. Hessami Pilehrood, T. Hessami Pilehrood. On sums of two rational cubes, Indian J. Pure Appl. Math. 36 (2005), no. 12, p. 707–717.
Kh. Hessami Pilehrood, T. Hessami Pilehrood. On the diophantine equation x^2+3=py^n, Indian J. Pure and Appl. Math. 36 (2005), no. 8, p. 431–439.
T. Hessami Pilehrood, Kh. Hessami Pilehrood. Lower bounds for linear forms in values of polylogarithms, Mat. Zametki, 2005, V. 77, no. 4, p. 623–629; English transl.: Math. Notes, 2005, V. 77, no. 4, p. 573–579.
Kh. Hessami Pilehrood, T. Hessami Pilehrood. On the diophantine equation x^2+3=py^{p-1} (in Russian), Chebyshevskii Sbornik, 2004, V. 5, no. 4 (12), p. 118–124.
Kh. Hessami Pilehrood, T. Hessami Pilehrood. On Mordell diophantine equation (in Russian), Chebyshevskii Sbornik, 2004, V. 5, no. 2 (10), p. 167–171.
T. Hessami Pilehrood, Kh. Hessami Pilehrood. Criteria for irrationality of generalized Euler's constant, J. of Number Theory, 2004, V. 108, no. 1, p. 169–185.
Kh. Hessami Pilehrood. On the Diophantine equation X^3+Y^3=PQZ^3, Moscow University Math. Bull. Ser. 1, no. 1, p. 19–22, 2001.
Kh. Hessami Pilehrood. On the Diophantine equation ax^3+bx^2+cx+dy+e=fxyz, Moscow University Math. Bull. Ser. 1, no. 1, p. 50–51, 2000.
M. Z. Garaev, Kh. Hessami Pilehrood. A note on the system of Pell's equations, Fundamentalnaya i Prikladnaya Matematika (Fundamental and Applied Mathematics). V. 5, no. 3, pp. 927–930, 1999.
Kh. Hessami Pilehrood. On the Diophantine equation x^2- Ny^2=-1, Moscow University Math. Bull. Ser. 1, no. 2, p. 65–67, 1999.
Т. Хессами Пилеруд, Х. Хессами Пилеруд, “Рациональные приближения значений дигамма-функции и гипотеза о знаменателях”, Матем. заметки, 90:5 (2011), 744–763; T. Hessami Pilehrood, Kh. Hessami Pilehrood, “Rational Approximations to Values of the Digamma Function and a Conjecture on Denominators”, Math. Notes, 90:5 (2011), 730–747
Т. Г. Хессами Пилеруд, Х. Хессами Пилеруд, “Об одной гипотезе Эрдеша”, Матем. заметки, 83:2 (2008), 312–315; T. G. Hessami Pilehrood, Kh. Hessami Pilehrood, “On a Conjecture of Erdős”, Math. Notes, 83:2 (2008), 281–284
Т. Г. Хессами Пилеруд, Х. Хессами Пилеруд, “Об иррациональности сумм дзета-значений”, Матем. заметки, 79:4 (2006), 607–618; T. G. Hessami Pilehrood, Kh. Hessami Pilehrood, “Irrationality of the sums of zeta values”, Math. Notes, 79:4 (2006), 561–571
Т. Г. Хессами Пилеруд, Х. Хессами Пилеруд, “Оценки снизу линейных форм от значений полилогарифмов”, Матем. заметки, 77:4 (2005), 623–629; T. G. Hessami Pilehrood, Kh. Hessami Pilehrood, “Lower bounds for linear forms in values of polylogarithms”, Math. Notes, 77:4 (2005), 573–579
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