Transcendental number theory, diophantine approximations, linear independence and irrationality of numbers, measures of irrationality and of transcendence, hypergeometric functions, polylogarithmic functions, Riemann zeta function, Pade approximations, number-theoretic remarkable constants.
• Moscow Institute of Electronics and Mathematics (1995-1998):
Analytical Geometry and Linear Algebra, Engineering Department
Linear Algebra II, Engineering Department .
Graph Theory, Department of Applied Mathematics.
• Shahrekord University (2001 - present):
Calculus1, Mathematics Department.
Mathematical Analysis 2, Mathematics Department.
Mathematical Analysis 3, Mathematics Department.
Complex Analysis, Mathematics Department.
Number Theory, Mathematics Department.
Topics in Number Theory, Mathematics Department.
English language for mathematicians, Mathematics Department.
[1]T. HessamiPilehrood. Lower bound for a linear form, Mat.Zametki V. 66 (1999), no.4, p.617-623; English transl.: Math. Notes. V. 66 (1999), no. 4, p.507-512.
[2] T. HessamiPilehrood. Linear independence of vectors with polylogarithmic coordinates, Vestnik Moskov. Univ.Ser.I Mat.Mekh. No 6. (1999), p.54-56; English transl.: Moscow Univ. Math. Bull. V. 54 (1999), no. 6, p.40-42.
[3]T. HessamiPilehrood. Lower bounds for linear forms in values of certain hypergeometric functions, Mat.Zametki. V. 67 (2000), no 3, p.441-451; English transl.: Math. Notes. V. 67 (2000), no 3, p.372-381. pdf Springer link
[4]T. HessamiPilehrood. On arithmetical properties of values of the polylogarithmic functions, Fundam. Prikl. Mat. V. 7 (2001), no 4, p.1237-1258. ps (Russian), Journal link
[5]T. Hessami Pilehrood, Kh. Hessami Pilehrood. Criteria for irrationality of generalized Euler's constant, J. Number Theory, (2004), V.108, no.1, p.169-185.
[6] Kh. Hessami Pilehrood, T. Hessami Pilehrood. On Mordell diophantine equation (in Russian), Chebyshevskii sbornik, (2004), V.5, no. 2 (10), p.167-171.
[7] Kh. Hessami Pilehrood, T. HessamiPilehrood. On the diophantine equation $x^2+3=py^{p-1},$ (in Russian), Chebyshevskii Sbornik, (2004), V.5, no. 4 (12), p.118-124.
[8] 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. pdf Springer link
[9] Kh. Hessami Pilehrood, T. HessamiPilehrood. On the diophantine equation $x^2+3=py^n,$ Indian J. Pure Appl. Math. V.36 (2005), no.8, p.431-439.
[10] Kh. Hessami Pilehrood, T. HessamiPilehrood. On sums of two rational cubes, Indian J. Pure Appl. Math. V. 36 (2005), no.12, p.707-717.
[11]T. Hessami Pilehrood, Kh. Hessami Pilehrood. Irrationality of the sums of zeta values, Mat. Zametki, V.79 (2006), no.4, p.607-618; English transl.: Math. Notes, V.79 (2006), no.4, p.561-571. pdf Springer link
[12] Kh. Hessami Pilehrood, T. Hessami Pilehrood, W.Zudilin. Irrationality of certain numbers that contain values of the di- and trilogarithm, Math. Zeitschrift, V. 254 (2006), no.2, p.299-313.
[13] Kh. Hessami Pilehrood, T. HessamiPilehrood. Arithmetical properties of some series with logarithmic coefficients, Math. Zeitschrift, V. 255 (2007), no.1, p.117-131.
[14] Kh. Hessami Pilehrood, T. HessamiPilehrood. On conditional irrationality measures for values of the digamma function, J. Number Theory, V. 123 (2007), no.1, p.241-253.
[16] Kh. Hessami Pilehrood, T. HessamiPilehrood. On a conjecture of Erdos,Mat. Zametki, (2008), V.83, no. 2, p.312-315; English transl.: Math. Notes, (2008), V.83, no. 2, p.281-284.
[17] Kh. Hessami Pilehrood, T. HessamiPilehrood. Generating function identities for $\zeta(2n+2), \zeta(2n+3)$ via the WZ metod, The Electronic Journal of Combinatorics.15 (2008), no. 1, #R35, p.1-9.
[18] Kh. Hessami Pilehrood, T. Hessami Pilehrood. An Apery-like continued fraction for $\pi\coth\pi,$ Journal of Difference Equations and Applications, 14 (2008), no. 12, p. 1279-1287.
[19] Kh. Hessami Pilehrood, T. Hessami Pilehrood. Simultaneous generation for zeta values by the Markov-MZ method, Discrete Mathematics and Theoretical Computer Science (DMTCS) 10:3, 2008, 115-124.arXiv:0801.3310[math.CO].
[20] Kh. Hessami Pilehrood, T. Hessami Pilehrood. Vacca-type series for values of the generalized-Euler constant function and its derivative, J. Integer Sequences, 13 (2010), Article 10.7.3 arXiv:0808.0410 [math.NT].
[21] Kh. Hessami Pilehrood, T. Hessami Pilehrood. Series acceleration formulas for beta values, Discrete Math. and Theoretical Computer Science (DMTCS) 12:2 (2010), 223-236.
[22] Kh. Hessami Pilehrood, T. HessamiPilehrood. Approximations to Euler's constant, Math. Ineq. and Appl. 13 (2010), no. 4, 761-773. arXiv:0708.2771 [math.NT].
[23] Kh. Hessami Pilehrood, T. HessamiPilehrood. A q-analogue of the Bailey- Borwein-Bradley identity, accepted for publication, to appear in J. Symbolic Computation (Elsevier); arXiv:0903.2843 [math. NT]
[24] Kh. Hessami Pilehrood, T. Hessami Pilehrood. Rational approximations for the quotient of gamma values, accepted for publication, to appear in Indagationes Mathematcae (Elsevier); arXiv:1010.0429v1 [math. NT]
[25] Kh. Hessami Pilehrood, T. Hessami Pilehrood. Rational approximations for values of the digamma function and a denominators conjecture, arXiv:1004.0578 [math. NT]
[26] Kh. Hessami Pilehrood, T. Hessami Pilehrood. On a continued fraction expansion for Euler's constant, arXiv:1010.1420 [math. NT]
[27] Kh. Hessami Pilehrood, T. Hessami Pilehrood. Rational approximations to values of Bell polynomials at points involving Euler's constant and zeta values.
[1] On linear independence of vectors with polylogarithmic coordinates. The 30th International Conference on Mathematics (Ardebil, Iran, September 1999).
[2] Lower bounds for linear forms in values of polylogarithms. The 33th International Conference on Mathematics (Mashhad, Iran, September 2002).
[3] On the positive integral solutions of a third degree Diophantine equation (with Kh. Hessami Pilehrood). The 34th Iranian Mathematics Conference (Shahrood, Iran, September 2003).
[4] On some Diophantine inequalities involving the hypergeometric functions (with Kh. Hessami Pilehrood). The 34th Iranian Mathematics Conference (Shahrood, Iran, September 2003).
[5] On Mordell diophantine equation (with Kh. Hessami Pilehrood). Sixth International conference ``Algebra and Number Theory: Modern Problems and Applications'' dedicated to 100-year anniversary of N. G. Chudakov (Saratov State University, Saratov, Russia, September 2004).
[6] Conditional irrationality measures for generalized Euler's constant (with Kh. Hessami Pilehrood). XXIV Journees Arithmetiques. (Marseille, France, 4-8 July 2005).
[7]On irrationality of sums of zeta values (with Kh. Hessami Pilehrood). XXIV Journees Arithmetiques. (Marseille, France, 4-8 July 2005).
[8] Approximation formulas for logarithms of some infinite products (with Kh. Hessami Pilehrood). International Congress of Mathematicians, ICM 2006. (Madrid, Spain, 22-30 August 2006).
[9] On irrationality of certain numbers that contain values of the di- and trilogarithm (with Kh. Hessami Pilehrood and W. Zudilin). International Congress of Mathematicians, ICM 2006. (Madrid, Spain, 22-30 August 2006).
[10] Apery-like recursion and continued fraction for $\pi\coth\pi$ (with Kh. Hessami Pilehrood). Conference on Diophantine approximations, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany, 15-21 April, 2007. Report No.21/2007, p.56-58.
[11] On transcendence of certain infinite series (with Kh. Hessami Pilehrood). 25th Journees Arithmetiques. (University of Edinburgh and ICMS, Edinburgh, Scotland, UK, 2-6 July, 2007).
[12] On Apery-like recursion and continued fraction for $\pi\coth\pi$ (with Kh. Hessami Pilehrood). 25th Journees Arithmetiques. (University of Edinburgh and ICMS, Edinburgh, Scotland, UK, 2-6 July, 2007).
[13] On transcendence of certain infinite series (with Kh. Hessami Pilehrood).ICTP preprint no. IC20070097.The Abdus Salam International Centre for Theoretical Physics, August 2007 pdfICTP link
[14] Approximations to Euler's constant (with Kh. Hessami Pilehrood).ICTP preprint no. IC20070098.The Abdus Salam International Centre for Theoretical Physics, August 2007 pdfICTP link
[15] Vacca-type series for values of the generalized-Euler-constant function and its derivative (with Kh. Hessami Pilehrood). Preprint of the Max-Planck-Institut fur Mathematik; MPIM2008-93. MPIM link.
[16] Series acceleration formulas for values of the Riemann zeta function, Number Theory Launch Seminar, Max-Planck-Institut fur Mathematik, Bonn, Germany, 20 August, 2008.
[17] Approximations to differences of digamma function values. International conference "Approximation and Computation 2008 "dedicated to Prof. G. V. Milovanovic' on the occasion of his 60-th anniversary. University of Nis', Serbia, August 25-29, 2008.
On–going research projects
Student supervision
[1] Davood Fatehi Ghahfarokhi (M.Sc. June, 2006).
[2] Sadegh Banitalebi (M.Sc. November, 2007).
[3] Sedighe Salehi (M.Sc. June, 2008).
[4] Hamideh Keshavarzi (M.Sc. June, 2008).
Useful Links
[1] Institute for Studies in Theoretical Physics and Mathematics (IPM).
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