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.
|Zeta measure associated to F_q[T]
J. Number Theory, 35 (1990), no. 1, 1-17.
|Tensor powers of the Carlitz module and Zeta values (Joint
with Greg Anderson)
Ann. of Math (2) 132 (1990), no. 1, 159-191.
|Gauss sums for Function Fields
J. Number Theory, 37 (1991), no.2, 242-252.
|Gamma functions for function fields and Drinfeld modules
Ann. of Math (2) 134 (1991), no.1, 25-64.
|Continued fraction for the exponential for F_q[T]
J. Number Theory, 41 (1992), no.2, 150-155.
|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).
|Shtukas and Jacobi sums
Invent. Math 111 (1993), no.3, 557-570.
|Behaviour of function field Gauss sums at infinity (Appendix by J. F. Voloch)
Bull. London Math Soc. 25(1993), 417-426
|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)
|On characteristic p zeta functions
Compositio Math. 99 no. 3 (1995), 231-247
|Hypergeometric functions for function fields
Finite Fields and their Applications 1 (1995), no.2, 219-231 (Carlitz Special issue)
|Automata-style proof of Voloch's result on transcendence
J. Number Theory, 58 (1996), no.1, 60-63.
|Exponential and continued fractions
J. Number Theory, 59 (1996), 248-261.
|Transcendence of Gamma values for F_q[t]
Annals of Math 144 (1996), 60-63.
|Patterns of continued fractions for the analogues of e and related numbers in function field case
J. Number Theory, 66(1997), 129-147.
|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).
|Computational classification of numbers and algebraic properties
(Joint with Robert Beals)
Internat. Math. Res. Notices 15 (1998), 799-818.
|Diophantine approximation exponents and continued fractions for algebraic power series
J. Number Theory, 79 (1999), 284-291.
|Automata and transcendence of the Tate period in finite characteristic (Joint with Jean-Paul Allouche)
Proc. Amer. Math. Soc, 127 (1999), 1309-1312.
| An alternate approach to solitons for F_q[t]
J. Number Theory, 76 (1999), 301-319.
| Hypergeometric functions for function fields II
J. Ramanujan Math. Soc. 15 No. 1 (2000), 43-52.
| Diophantine approximation and deformation (Joint with M. Kim and J. F. Voloch)
Bull. Soc. Math. France 128 (2000), 585-598.
| Integrable systems and number theory in finite characteristic
Physica D, 152-153 (2001), 1-8. (Advances in nonlinear mathematics and science, special issue).
| Elliptic curves in function field arithmetic
Current trends in Number Theory, Ed. S. Adhikari et al, (2002), 215-238. (Almost identical to final version).
|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)
|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)
|Diophantine approximation and Transcendence in
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)
|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)
|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
| Relations between multizeta values for F_q[T]
International Math Research Notices IMRN (2009), no. 12, 2318-2346.
| 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.
| Power sums with applications to multizeta and zeta zero distribution
Finite Fields and Their Applications 15 (2009) 534-552
| 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.
| 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).
| Shuffle relations for function field multizeta values
International Mathematics Research Notices IMRN (2010), No. 11, 1973-1980.
|Higher Diophantine Approximation Exponents and Continued Fraction
Symmetries for Function Fields
Proceedings of Amer Math Soc. vol.139 no.1, (2011), 11-19.
| 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)
| A note on Numerators of Bernoulli numbers
Proc. Amer. Math. Soc. 140 (2012) no. 11, 3673-3676
| 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.
|Binomial and Factorial congruences for F_q[t] Finite Fields and Their Applications 18 (2012) 271-282.|
From rationality to transcendence in finite characteristic
Journ\'ees Annuelles Soci\'et\'e Math\'ematique de France (2012), p. 21-48
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)
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
|Higher Diophantine Approximation Exponents and Continued Fraction Symmetries for Function Fields II Proceedings of American Mathematical Society 141 (2013) no. 8, 2603-2608.|
|Differential characterization of Wilson primes for F_q[t] Algebra and Number Theory, Vol. 7 No. 8 (2013), 1841-1848.|
| 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.
| 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)
|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.|
|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.|
| Multiplicative relations between coefficients of logarithmic derivatives of F_q-linear functions and applications (Joint with Alejandro
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.
| Multizeta shuffle relations for function fields with non rational infinite place (Joint with Alejandro
Finite Fields and their applications 37 (2016), 344-356.
| Leading coefficient of the Goss zeta value and p-ranks of Jacobians of Carlitz cyclotomic covers
(Joint with Gebhard Boeckle)
Journal de Theorie des Nombres de Bordeaux 29 (2017) 963-995 (Special volume in honor of David Goss) Final submitted version.
| Multizeta values for function fields: A survey
Journal de Theorie des Nombres de Bordeaux 29 (2017) 997-1023 (Special volume in honor of David Goss) Final submitted version.
| Kaprekar Phenomena
Proceeding of Ropar Conference (Number Theory: Arithmetic, Diophantine and Transcendence), Ramanujan Math Society-Lecture Notes Series No. 26, (2019), pp. 1-10.
| Remembering John Tate
Resonance, Indian Academy of Sciences, Vol. 25, Feb. 2020, pp. 177-190
| Automata methods in transcendence (Based on
minicourse at ETH and lectures at Banff workshop)
In t-Motives: Hodge structures, transcendence and other motivic aspects, pp. 351-372, Ed. by Bockle, Goss, Hartl, Papanikolas, European Math. Soc. pub. May 2020. Final submitted version.
|Multizeta in function field arithmetic
In t-motives: Hodge structures, transcendence and other motivic aspects, pp. 441-452, Ed. by Bockle, Goss, Hartl, Papnikolas, European Math. Soc. pub. May 2020. Final submitted version.
|Zetalike multizeta values for higher genus curves (Joint with Alejandro Lara Rodriguez)
Journal de Theorie des Nombres de Bordeaux, 33 (2021)553-581. Final submitted version.
|Surprising symmetries in distribution of prime polynomials
Arxive preprint with minor updates.
| Expected Mordell-Weil rank heuristics through Sato-Tate, Birch and Swinnerton-Dyer conjectures
Arxive preprint 21 October 2022. Updated 2 November 22
| Fermat-Wilson Supercongruences, arithmetic derivatives and strange factorizations
Arxive preprint 2 November 2022.