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.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. Elsevier link
[6] Kh. Hessami Pilehrood, T. Hessami Pilehrood. On Mordell diophantine equation (Russian), Chebyshevskii sbornik, (2004), V.5, no. 2 (10), p.167-171.
[7] Kh. Hessami Pilehrood, T. HessamiPilehrood. On the diophantine equation $x^2+3=py^{p-1},$ (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. HessamiPilehrood, 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. Springer link
[13] Kh. Hessami Pilehrood, T. HessamiPilehrood. Arithmetical properties of some series with logarithmic coefficients, Math. Zeitschrift, V. 255 (2007), no.1, p.117-131. Springer link
[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. Elsevier link
[15] Kh. Hessami Pilehrood, T. Hessami Pilehrood. Infinite sums as linear combinations of polygamma functions, Acta Arithmetica. 130, No. 3, 231-254 (2007). pdf ps
[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. pdf (English), ps (Russian), Springer link
[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 occation 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).
[5] Azam Baiaty, (M.Sc. September, 2010).
Useful Links
[1] Institute for Studies in Theoretical Physics and Mathematics (IPM).
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