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- Dinesh S. Thakur
- 2008

Z = {integers} Q = {rational numbers} R = {real numbers} C = {complex numbers} Z+ = { positive integers} q = a power of a prime p Fq = A Finite field with q elements A = Fq[t] A+ = {monics in A} K =â€¦ (More)

- Dinesh S. Thakur, Zhi-Ying Wen, Jia-Yan Yao, Liang Zhao, Jean-Pierre Kahane
- 2009

We study hypergeometric functions for Fq [T ], and show in the entire (non-polynomial) case the transcendence of their special values at nonzero algebraic arguments which generate extension of theâ€¦ (More)

Let Ïˆ(x) denote the digamma function, that is, the logarithmic derivative of Eulerâ€™s -function. Let q be a positive integer greater than 1 and Î³ denote Eulerâ€™s constant. We show that all the numbersâ€¦ (More)

- Dinesh S. Thakur
- 2009

In contrast to Rothâ€™s theorem that all algebraic irrational real numbers have approximation exponent two, the distribution of the exponents for the function field counterparts is not evenâ€¦ (More)

Despite the failure of naive analogs of the sum shuffle or the integral shuffle relations, we prove the existence of â€˜shuffleâ€™ relations for the multizeta values (for a general A, with a rationalâ€¦ (More)

- Dinesh S. Thakur
- 1996

The continued fraction expansion of a real number is a fundamental and revealing expansion through its connection with Euclidean algorithm and with ``best'' rational approximations (see [HW]). At theâ€¦ (More)

- Minhyong Kim, Dinesh S. Thakur, JosÃ© Luis Felipe, VOLOCH
- 2001

â€” It is well-known that while the analogue of Liouvilleâ€™s theorem on diophantine approximation holds in finite characteristic, the analogue of Rothâ€™s theorem fails quite badly. We associate certainâ€¦ (More)

- Praveen Vasudevan, Dinesh S. Thakur
- Applied biochemistry and biotechnology
- 1994

This article examines the effect of pressure on the steady-state kinetics and long-term deactivation of the enzyme catalase supported on porous alumina. The reaction studied is the decomposition ofâ€¦ (More)

- Dinesh S. Thakur
- Finite Fields and Their Applications
- 2009

Article history: Received 18 November 2008 Revised 1 April 2009 Available online 22 April 2009 Communicated by Neal Koblitz

- Dinesh S. Thakur
- 1996

For more on the Tate curve (which we will not use directly) and for standard facts on modular forms (which we will use later), see [S, Chap. 5; M. Chap. 1], respectively. Voloch's nice proof involvedâ€¦ (More)