과제정보
연구 과제 주관 기관 : Inha University
참고문헌
- J. Allouche and J. Shallit, Automatic sequences, Theory, applications, generalizations, Cambridge University Press, Cambridge, 2003.
- B. Angles and F. Pellarin, Universal Gauss-Thakur sums and L-series, Invent. Math. 200 (2015), no. 2, 653-669. https://doi.org/10.1007/s00222-014-0546-8
- V. Bosser and F. Pellarin, Hyperdifferential properties of Drinfeld quasi-modular forms, Int. Math. Res. Not. IMRN 2008 (2008), no. 11, Art. ID rnn032, 56 pp.
- A. Bostan and P. Dumas, Wronkians and linear independence, Amer. Math. Monthly 117 (2010), no. 8, 722-727. https://doi.org/10.4169/000298910x515785
- L. Carlitz, A set of polynomials, Duke Math. J. 6 (1940), 486-504. https://doi.org/10.1215/S0012-7094-40-00639-1
- P. Cartier, Une nouvelle operation sur les formes differentielles C. R. Acad. Sci. Paris 244 (1957), 426-428.
- P. Cartier, Questions de rationalite des diviseurs en geometrie algebrique, Bull. Soc. Math. France 86 (1958), 177-251.
- G. Christol, Ensembles presque periodiques k-reconnaissables, Theoret. Comput. Sci. 9 (1979), no. 1, 141-145. https://doi.org/10.1016/0304-3975(79)90011-2
- K. Conrad, A q-Analogue of Mahler Expansions I, Adv. Math. 153 (2000), no. 2, 185-230. https://doi.org/10.1006/aima.1999.1890
- K. Conrad, The digit principle, J. Number Theory 84 (2000), no. 2, 230-257. https://doi.org/10.1006/jnth.2000.2507
- A. Garcia and J. F. Voloch, Wronskians and linear independence in fields of prime characteristic, Manuscripta Math. 59 (1987), no. 4, 457-469. https://doi.org/10.1007/BF01170848
- D. Goss, Fourier series, Measures and Divided Power Series in the theory of Function Fields, K-theory 1 (1989), no. 4, 533-555.
- L. Hasse and F. K. Schmidt, Noch eine Begrundung der Theorie der hoheren Diffenentialquotienten in einem algrbraischen Funktionenkorper einer Unbestimmten, J. Reine Angew. Math. 177 (1937), 215-237.
-
J. Jang, S. Jeong, and C. Li, Criteria of measure-preservation for 1-Lipschitz functions on
$F_q[[T]]$ in terms of the van der Put basis and its applications, Finite Fields Appl. 37 (2016), 131-157. https://doi.org/10.1016/j.ffa.2015.09.007 - S. Jeong, A comparison of the Carlitz and digit derivatives bases in function field arithmetic, J. Number Theory 84 (2000), no. 2, 258-275. https://doi.org/10.1006/jnth.2000.2527
-
S. Jeong, Continuous Linear Endomorphisms and Difference Equations over the Completion of
$F_q[T]$ , J. Number Theory 84 (2000), no. 2, 276-291. https://doi.org/10.1006/jnth.2000.2532 - S. Jeong, Hyperdifferential operators and continuous functions on function fields, J. Number Theory 89 (2001), no. 1, 165-178. https://doi.org/10.1006/jnth.2000.2629
- S. Jeong, Digit derivatives and application to zeta measures, Acta Arith. 112 (2004), no. 3, 229-245. https://doi.org/10.4064/aa112-3-2
- S. Jeong, Calculus in positive characteristic p, J. Number Theory 131 (2011), no. 6, 1089-1104. https://doi.org/10.1016/j.jnt.2010.12.006
-
S. Jeong, Shift operators and two applications to
$F_q[[T]]$ , J. Number Theory 133 (2013), no. 9, 2874-2891. https://doi.org/10.1016/j.jnt.2013.02.006 -
S. Jeong, Characterization of ergodicity of T -adic maps on
$F_2[[T]]$ using digit derivatives basis, J. Number Theory 133 (2013), no. 6, 1846-1863. https://doi.org/10.1016/j.jnt.2012.11.009 - E. Lucas, Sur les congruences des nombres euleriens et des coefficients differentiels des fonctions trigonometriques, suivant un module premier, Bull. Soc. Math. France 6 (1878), 49-54.
- M. A. Papanikolas, Log-algebraicity on tensor powers of the Carlitz module and special values of Goss L-functions, preprint.
- A. M. Robert, A course in p-adic analysis, Vol. 198 GTM, Springer-Verlag, New York, 2000.
- F. K. Schmidt, Die Wronskische Determinante in beliebigen differenzierbaren Funktionenkorpern, Math. Z. 45 (1939), no. 1, 62-74. https://doi.org/10.1007/BF01580273
- J. P. Serre, Endomorphismes completement continus des espaces de Banach p-adiques, Inst. Hautes Etudes Sci. Publ. Math. 12 (1962), 69-85. https://doi.org/10.1007/BF02684276
- H. Sharif and C. Woodcock, Algebraic functions over a field of positive characteristic and Hadamard products, J. London Math. Soc. (2) 37 (1988), no. 3, 395-403.
- B. Snyder, Hyperdifferential Operators on Function Fields and Their Applications, The Ohio State University (Columbus), Ph. D. Thesis, 1999.
- J. F. Voloch, Differential operators and interpolation series in power series fields, J. Number Theory 71 (1998), no. 1, 106-108. https://doi.org/10.1006/jnth.1998.2241
-
C. G. Wagner, Interpolation series for continuous functions on
${\pi}$ -adic completions of GF(q, x), Arta Arith. 17 (1971), 389-406. https://doi.org/10.4064/aa-17-4-389-406 - C. G. Wagner, Linear operators in local fields of prime characteristic, J. Jeine Angew. Math. 251 (1971), 153-160.
-
Z. Yang,
$C^n$ -functions over completions of$F_r[T]$ at finite places of$F_r(T)$ , J. Number Theory 108 (2004), no. 2, 346-374. https://doi.org/10.1016/j.jnt.2004.05.007