D  I  N  E  S  H      S.       T  H  A  K  U  R  



Here are some .pdf files of published papers. If you have any corrections/comments, please look at the corrections/updates links on my homepage, 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.
pdf
Zeta measure associated to F_q[T]
J. Number Theory, 35 (1990), no. 1, 1-17.
pdf
Tensor powers of the Carlitz module and Zeta values (Joint with Greg Anderson)
Ann. of Math (2) 132 (1990), no. 1, 159-191.
pdf
Gauss sums for Function Fields
J. Number Theory, 37 (1991), no.2, 242-252.
pdf
Gamma functions for function fields and Drinfeld modules
Ann. of Math (2) 134 (1991), no.1, 25-64.
pdf
Continued fraction for the exponential for F_q[T]
J. Number Theory, 41 (1992), no.2, 150-155.
pdf
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).
pdf
Shtukas and Jacobi sums
Invent. Math 111 (1993), no.3, 557-570.
pdf
Behaviour of function field Gauss sums at infinity (Appendix by J. F. Voloch)
Bull. London Math Soc. 25(1993), 417-426
pdf
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)
pdf
On characteristic p zeta functions
Compositio Math. 99 no. 3 (1995), 231-247
pdf
Hypergeometric functions for function fields
Finite Fields and their Applications 1 (1995), no.2, 219-231 (Carlitz Special issue)
pdf
Automata-style proof of Voloch's result on transcendence
J. Number Theory, 58 (1996), no.1, 60-63.
pdf
Exponential and continued fractions
J. Number Theory, 59 (1996), 248-261.
pdf
Transcendence of Gamma values for F_q[t]
Annals of Math 144 (1996), 60-63.
pdf
Patterns of continued fractions for the analogues of e and related numbers in function field case
J. Number Theory, 66(1997), 129-147.
pdf
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).
pdf
Computational classification of numbers and algebraic properties (Joint with Robert Beals)
Internat. Math. Res. Notices 15 (1998), 799-818.
pdf
Diophantine approximation exponents and continued fractions for algebraic power series
J. Number Theory, 79 (1999), 284-291.
pdf
Automata and transcendence of the Tate period in finite characteristic (Joint with Jean-Paul Allouche)
Proc. Amer. Math. Soc, 127 (1999), 1309-1312.
pdf
An alternate approach to solitons for F_q[t]
J. Number Theory, 76 (1999), 301-319.
pdf
Diophantine approximation and deformation (Joint with M. Kim and J. F. Voloch)
Bull. Soc. Math. France 128 (2000), 585-598.
pdf
Integrable systems and number theory in finite characteristic
Physica D, 152-153 (2001), 1-8. (Advances in nonlinear mathematics and science, special issue).
pdf
Elliptic curves in function field arithmetic
Current trends in Number Theory, Ed. S. Adhikari et al, (2002), 215-238. (Almost identical to final version).
pdf
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)
pdf
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)
pdf
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)
pdf
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)
pdf
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
pdf
Relations between multizeta values for F_q[T]
International Math Research Notices IMRN (2009), no. 12, 2318-2346.
pdf
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.
pdf
Power sums with applications to multizeta and zeta zero distribution for F_q[t]
Finite Fields and Their Applications 15 (2009) 534-552
pdf
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.
pdf
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).
pdf
Shuffle relations for function field multizeta values
International Mathematics Research Notices IMRN (2010), No. 11, 1973-1980.
pdf
Higher Diophantine Approximation Exponents and Continued Fraction Symmetries for Function Fields
Proceedings of Amer Math Soc. vol.139 no.1, (2011), 11-19.
pdf
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)
pdf
A note on Numerators of Bernoulli numbers
Proc. Amer. Math. Soc. 140 (2012) no. 11, 3673-3676
pdf
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.
pdf
Binomial and Factorial congruences for F_q[t] Finite Fields and Their Applications 18 (2012) 271-282. pdf
From rationality to transcendence in finite characteristic
Journ\'ees Annuelles Soci\'et\'e Math\'ematique de France (2012), p. 21-48
pdf
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)
pdf
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
(Corrected submitted version as on the journal site, with minor corrections as mentioned in updates file to the first published version)
pdf
Higher Diophantine Approximation Exponents and Continued Fraction Symmetries for Function Fields II Proceedings of American Mathematical Society 141 (2013) no. 8, 2603-2608. pdf
Differential characterization of Wilson primes for F_q[t] Algebra and Number Theory, Vol. 7 No. 8 (2013), 1841-1848. pdf
Zeta-like multizeta values for F_q[t] (Joint with Alejandro Lara Rodriguez)
Indian J. Pure Appl. Math. 45 (5):785-798 (2014), Indian National Science Academy, Ramanujan Special Volume. On arxives also.
pdf
Arithmetic of Gamma, Zeta and Multizeta values for Function Fields
In the book `Arithmetic geometry over Global Function Fields' (Series: Advanced courses in Mathematics, CRM, Barcelona), Birkhauser, Springer-Bassel 2014. (Unprocessed submitted version)
pdf
Fermat versus Wilson congruences, Arithmetic derivatives and Zeta Values. Special volume `Second decade of FFA' of Finite Fields and their Applications 32 (2015) 192-206. pdf
Power sums of polynomials over finite fields and applications: A survey. Special volume `Second decade of FFA' of Finite Fields and their Applications 32 (2015) 171-191. pdf
Multiplicative relations between coefficients of logarithmic derivatives of F_q-linear functions and applications (Joint with Alejandro Lara Rodriguez)
Journal of Algebra and its applications (Special issue in Honor of Shreeram S. Abhyankar), Vol 14, No. 9, (2015), 154006 (13 pages). On arxives also.
pdf
Multizeta shuffle relations for function fields with non rational infinite place (Joint with Alejandro Lara Rodriguez)
Finite Fields and their applications 37 (2016), 344-356.
pdf
Leading coefficient of the Goss zeta value and p-ranks of Jacobians of Carlitz cyclotomic covers (Joint with Gebhard Boeckle)
To appear in Journal de Theorie des Nombres de Bordeaux (Special volume in honor of David Goss) Final submitted version.
pdf
Multizeta values for function fields: A survey
To appear in Journal de Theorie des Nombres de Bordeaux (Special volume in honor of David Goss) Final submitted version.
pdf
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. Final submitted version.
pdf
Multizeta in function field arithmetic
To appear in proceedings of 2009 Banff workshop to be published by EMS. Final submitted version.
pdf
Surprising symmetries in distribution of prime polynomials
Arxive preprint with minor updates.
pdf