Inspired by the classical setting, Goss defined
Inspiré par le cadre classique, Goss a défini des séries
Révisé le :
Accepté le :
Publié le :
Mots-clés : Drinfeld modules,
Oğuz Gezmiş 1

@article{JTNB_2021__33_2_511_0, author = {O\u{g}uz Gezmi\c{s}}, title = {Special values of {Goss} $L$-series attached to {Drinfeld} modules of rank 2}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {511--552}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {33}, number = {2}, year = {2021}, doi = {10.5802/jtnb.1168}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1168/} }
TY - JOUR AU - Oğuz Gezmiş TI - Special values of Goss $L$-series attached to Drinfeld modules of rank 2 JO - Journal de théorie des nombres de Bordeaux PY - 2021 SP - 511 EP - 552 VL - 33 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1168/ DO - 10.5802/jtnb.1168 LA - en ID - JTNB_2021__33_2_511_0 ER -
%0 Journal Article %A Oğuz Gezmiş %T Special values of Goss $L$-series attached to Drinfeld modules of rank 2 %J Journal de théorie des nombres de Bordeaux %D 2021 %P 511-552 %V 33 %N 2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1168/ %R 10.5802/jtnb.1168 %G en %F JTNB_2021__33_2_511_0
Oğuz Gezmiş. Special values of Goss $L$-series attached to Drinfeld modules of rank 2. Journal de théorie des nombres de Bordeaux, Tome 33 (2021) no. 2, pp. 511-552. doi : 10.5802/jtnb.1168. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1168/
[1]
[2] Tensor powers of the Carlitz module and zeta values, Ann. Math., Volume 132 (1990) no. 1, pp. 159-191 | DOI | MR | Zbl
[3] A class formula for admissible Anderson modules (2020) (https://hal.archives-ouvertes.fr/hal-02490566)
[4] On special
[5] Recent developments in the theory of Anderson modules, Acta Math. Vietnam., Volume 45 (2020) no. 1, pp. 199-216 | DOI | MR | Zbl
[6] Arithmetic of function field units, Math. Ann., Volume 367 (2017) no. 1-2, pp. 501-579 | DOI | MR | Zbl
[7] Cohomological Theory of Crystals over Function Fields, EMS Tracts in Mathematics, 9, European Mathematical Society, 2009 | MR | Zbl
[8] Linear independence and divided derivatives of a Drinfeld module. I., Number Theory in Progress, Vol. 1 (Zakopane-Kościelisko, 1997), Volume 1, Walter de Gruyter, 1997, pp. 47-61 | Zbl
[9] A rapid introduction to Drinfeld modules,
[10] On certain functions connected with polynomials in a Galois field, Duke Math. J., Volume 1 (1935) no. 2, pp. 137-168 | MR | Zbl
[11] A class of polynomials, Trans. Am. Math. Soc., Volume 43 (1938) no. 2, pp. 167-182 | DOI | Zbl
[12] Log-algebraic identities on Drinfeld modules and special
[13] Taylor coefficients of Anderson-Thakur series and explicit formulae, Math. Ann., Volume 379 (2021) no. 3-4, pp. 1425-1474 | DOI | MR | Zbl
[14] On multiple polylogarithms in characteristic
[15] The digit principle, J. Number Theory, Volume 84 (2000) no. 2, pp. 230-257 | DOI | MR | Zbl
[16] Towards a class number formula for Drinfeld modules, Ph. D. Thesis, University of Amsterdam / KU Leuven (2016) (available at http://hdl.handle.net/11245/1.545161)
[17] La conjecture de Weil. I., Publ. Math., Inst. Hautes Étud. Sci., Volume 43 (1974), pp. 273-307 | DOI | Numdam | Zbl
[18] Explicit formulas for Drinfeld modules and their periods, J. Number Theory, Volume 133 (2013) no. 6, pp. 1864-1886 | DOI | MR | Zbl
[19] Special
[20] Binomial coefficients modulo a prime, Am. Math. Mon., Volume 54 (1947) no. 10, pp. 589-592 | DOI | MR | Zbl
[21]
[22] Deformation of multiple zeta values and their logarithmic interpretation in positive characteristic, Doc. Math., Volume 25 (2020), pp. 2355-2411 | MR | Zbl
[23]
[24] Basic Structures of Function Field Arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge., 35, Springer, 1996 | MR | Zbl
[25] Tensor products of Drinfeld modules and
[26] Pink’s theory of Hodge structures and the Hodge conjecture over function fields,
[27] Explicit class field theory for rational function fields, Trans. Am. Math. Soc., Volume 189 (1974), pp. 77-91 | DOI | MR | Zbl
[28] On characteristic polynomials of geometric Frobenius associated to Drinfeld modules, Compos. Math., Volume 122 (2000) no. 3, pp. 261-280 | DOI | MR | Zbl
[29] The Hodge Conjecture for Function Fields, Ph. D. Thesis, University of Muenster (2010)
[30] Abelian varieties,
[31] Shtuka cohomology and special values of Goss L-functions, Ph. D. Thesis, University of Amsterdam (2018) (available at http://hdl.handle.net/1887/61145)
[32] Log-algebraicity on tensor powers of the Carlitz module and special values of Goss
[33] Abelian
[34] Algebraic monodromy groups of
[35] On
[36] Artin
[37] Special
[38] Special
[39]
[40] Function Field Arithmetic, World Scientific, 2004 | Zbl
[41] Function field modular forms and higher-derivations, Math. Ann., Volume 311 (1998) no. 3, pp. 439-466 | DOI | MR | Zbl
Cité par Sources :