D I N E S H S. T H A K U R
THIS WEBPAGE IS NO LONGER UPDATED. PLEASE SEE MY UROCHESTER WEBPAGE. Here are some .pdf files of published papers in final form, unless stated otherwise. If you have any corrections/comments, please look at the corrections/updates links and please let me know, if they have not been noticed. I will put all my papers online soon. For .pdf of papers in the book `Cyclotomic Fields' follow that book link.
| Gauss sums for F_q[t]
Invent. Math 94 (1988) no. 1, 105-112. |
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| Zeta measure associated to F_q[T] J. Number Theory, 35 (1990), no. 1, 1-17. |
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| Tensor powers of the Carlitz module and Zeta values (Joint
with Greg Anderson) Ann. of Math (2) 132 (1990), no. 1, 159-191. |
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| Gauss sums for Function Fields J. Number Theory, 37 (1991), no.2, 242-252. |
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| Gamma functions for function fields and Drinfeld modules Ann. of Math (2) 134 (1991), no.1, 25-64. |
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| Continued fraction for the exponential for F_q[T] J. Number Theory, 41 (1992), no.2, 150-155. |
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| Drinfeld modules and the arithmetic in function fields Internat. Math. Res. Notices (1992), no. 9, 185-197. (For the missing abstract, see abstracts link on homepage). |
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| Shtukas and Jacobi sums Invent. Math 111 (1993), no.3, 557-570. |
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| Behaviour of function field Gauss sums at infinity (Appendix by J. F. Voloch) Bull. London Math Soc. 25(1993), 417-426 |
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| Iwasawa theory and cyclotomic function fields Proceedings of conference on Arithmetic Geometry, Contemp Math 174 (1994), 157-165. (Ed. by J. Jones, N. Childress) (Almost identical to final version) |
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| On characteristic p zeta functions Compositio Math. 99 no. 3 (1995), 231-247 |
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| Hypergeometric functions for function fields Finite Fields and their Applications 1 (1995), no.2, 219-231 (Carlitz Special issue) |
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| Automata-style proof of Voloch's result on transcendence J. Number Theory, 58 (1996), no.1, 60-63. |
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| Exponential and continued fractions J. Number Theory, 59 (1996), 248-261. |
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| Transcendence of Gamma values for F_q[t] Annals of Math 144 (1996), 60-63. |
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| Patterns of continued fractions for the analogues of e and related numbers in function field case J. Number Theory, 66(1997), 129-147. |
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| Automata and Transcendence Number theory, Ed. by V. Kumar Murty and M. Waldschmidt, Contemp. Math. 210(1997), 387-399. Proc. of International conference on discrete math and number theory. (Almost identical to final version). |
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| Computational classification of numbers and algebraic properties
(Joint with Robert Beals) Internat. Math. Res. Notices 15 (1998), 799-818. |
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| Diophantine approximation exponents and continued fractions for algebraic power series J. Number Theory, 79 (1999), 284-291. |
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| Automata and transcendence of the Tate period in finite characteristic (Joint with Jean-Paul Allouche) Proc. Amer. Math. Soc, 127 (1999), 1309-1312. |
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| An alternate approach to solitons for F_q[t] J. Number Theory, 76 (1999), 301-319. |
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| Diophantine approximation and deformation (Joint with M. Kim and J. F. Voloch) Bull. Soc. Math. France 128 (2000), 585-598. |
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| Integrable systems and number theory in finite characteristic Physica D, 152-153 (2001), 1-8. (Advances in nonlinear mathematics and science, special issue). |
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| Elliptic curves in function field arithmetic Current trends in Number Theory, Ed. S. Adhikari et al, (2002), 215-238. (Almost identical to final version). |
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| Diophantine approximation in finite characteristic Algebra, Arithmetic and Geometry with Applications, Ed. C. Christensen et al, Springer 2003, 757-765. (Almost identical to final version) |
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| Recent developments in function field arithmetic The Mathematics Student, Vol. 76, 1-4 (2007), 163-170. Indian Mathematical Society (Centenary meeting talks) (Almost identical to final version but with wrong page numbers and formatting) |
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| Diophantine approximation and Transcendence in
finite characteristic in Diophantine Equations, Ed. N. Saradha, 265-278 (2008) Pub. for Tata Institute of Fundamental Research by Narosa Pub. (Almost identical to final version but with wrong page numbers) |
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| Approximation Exponents for function fields In Analytic Number Theory --Essays in Honor of Klaus Roth, Ed. by W. Chen, T. Gowers, H. Halbertam, W. Schmidt, R. Vaughn, Camb. U. Press (2009), 421-435. (Almost identical to published version) |
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| Multizeta values for F_q[t], their period interpretation and relations
between them(Joint with Greg Anderson) International Math Research Notices, IMRN (2009) no. 11, 2038-2055 |
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| Relations between multizeta values for F_q[T] International Math Research Notices IMRN (2009), no. 12, 2318-2346. |
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| Hypergeometric functions for function fields and transcendence
(Joint with Z. Wen, J. Yao, L. Zhao) CR Acad Sci. Paris, Ser. I 347 (2009), 467-472. |
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| Power sums with applications to multizeta and zeta zero distribution
for F_q[t]
Finite Fields and Their Applications 15 (2009) 534-552 |
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| Algebraic independence of arithmetic gamma values and Carlitz
zeta values (Joint with C. Chang, M. Papanikolas, J. Yu)
Advances in Mathematics 223 (2010), 1137-1154 (Final submitted version) |
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| Recent Progress and Open Problems in Function Field Arithmetic--
The Influence of John Tate's Work
Pure and Applied Mathematic Quarterly Vol. 6 No. 1 (Special Issue: In honor of John Tate, part 2 of 2), 1-20 (2010). |
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| Shuffle relations for function field multizeta values (Final
accepted version)
International Mathematics Research Notices IMRN (2010), No. 11, 1973-1980. |
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| Higher Diophantine Approximation Exponents and Continued Fraction
Symmetries for Function Fields
Proceedings of Amer Math Soc. vol.139 no.1, (2011), 11-19. (Final accepted version). |
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| Transcendence in positive characteristic and special
values of hypergeometric functions (Joint with Zhi-Ying Wen,
Jia-Yan Yao and Liang Zhao)
(Crelle's Journal) J. Reine Angew Math 657 (2011), 135-171. (Final accepted version) |
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| A note on Numerators of Bernoulli numbers
Proc. Amer. Math. Soc. 140 (2012) no. 11, 3673-3676 (Final accepted version) |
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| Infinitude of Elliptic Carmichael numbers (Joint
with Aaron Ekstrom and Carl Pomerance)
Unprocessed submitted version, J. Australian Math. Soc. 92 (2012) no.1, 45-60, special issue in memory of van der Poorten. |
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| Binomial and Factorial congruences for F_q[t]
Finite Fields and Their Applications 18 (2012) 271-282.
(Accepted unprocessed version). |
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From rationality to transcendence in finite characteristic
Journ\'ees Annuelles Soci\'et\'e Math\'ematique de France (2012), p. 21-48 |
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Infinitude of Wilson primes for F_q[t]
(Joint with Jim Sauerberg, Linghsueh Shu and George Todd) (Unprocessed submitted version) Acta Arith. 157 no. 1, 91-100 (2013) |
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Valuations of v-adic Power Sums and Zero Distribution for the Goss v-adic
Zeta Function for F_q[t]
Journal of Integer Sequences, Special Issue in Honor of the
60th Birthday of Jean-Paul Allouche, 16 (2013), Ar. 13.2.13, 1-18 (Unprocessed final version) |
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| Automata methods in transcendence (Based on
minicourse at ETH and lectures at 2009 Banff workshop)
To appear in proceedings of 2009 Banff workshop to be published by EMS. |
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| Multizeta in function field arithmetic
To appear in proceedings of 2009 Banff workshop to be published by EMS. |
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| Arithmetic of Gamma, Zeta and Multizeta values for Function Fields
To appear in CRM Advanced courses (2010) in Mathematics series books by Birkhauser (Unprocessed submitted version) |
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| Higher Diophantine Approximation Exponents and Continued Fraction Symmetries for Function Fields II (Accepted unprocessed version) Proc. Amer. Math. Soc. 141 (2013) no. 8, 2603-2608. | |||
| Differential characterization of Wilson primes for F_q[t] To appear in Algebra and Number Theory. |