Some mixed character sum identities of Katz II
Tóm tắt
Từ khóa
Tài liệu tham khảo
Amburg, I., Sharma, R., Sussman, D.M., Wootters, W.K.: States that “look the same” with respect to every basis in a mutually unbiased set. J. Math. Phys. 55(12), 122206 (2014)
Barman, R., Kalita, G.: Hyperelliptic curves over $$\mathbb{F}_q$$ F q and Gaussian hypergeometric series. J. Ramanujan Math. Soc. 30, 331–348 (2015)
Barman, R., Saikia, N.: On the polynomials $$x^d+ax^i+b$$ x d + a x i + b and $$x^d+ax^{d-i}+b$$ x d + a x d - i + b over $$\mathbb{F}_q$$ F q and Gaussian hypergeometric series. Ramanujan J. 35, 427–441 (2014)
Beilinson, A., Bernstein, J., Deligne, P.: Faisceaux pervers, Analyse et topologie sur les éspaces singuliers, I (Conférence de Luminy, 1981), Astérisque 100. Soc. Math. France, Paris (1982)
Berndt, B.C., Evans, R.J., Williams, K.S.: Gauss and Jacobi sums. Wiley-Interscience, New York (1998)
Deligne, P.: La conjecture de Weil II. Publ. Math. IHES 52, 313–428 (1981)
El-Guindy, A., Ono, K.: Hasse invariants for the Clausen elliptic curves. Ramanujan J. 31, 3–13 (2013)
Evans, R.J., Greene, J.R.: Evaluations of hypergeometric functions over finite fields. Hiroshima Math. J. 39, 217–235 (2009)
Evans, R.J., Greene, J.R.: A quadratic hypergeometric $${}_2F_1$$ 2 F 1 transformation over finite fields, Proc. Amer. Math. Soc. 145, 1071–1076 (2017)
Fuselier, J., Long, L., Ramakrishna, R., Swisher, H., Tu, F.-T.: Hypergeometric functions over finite fields, arXiv:1510.02575
Greene, J.R.: Hypergeometric functions over finite fields. Trans. Amer. Math. Soc. 301, 77–101 (1987)
Katz, N.M.: Rigid local systems and a question of Wootters. Commun. Number Theory Phys. 6(2), 223–278 (2012)
McCarthy, D., Papanikolas, M.: A finite field hypergeometric function associated to eigenvalues of a Siegel eigenform. Int. J. Number Theory 11, 2431–2450 (2015)
Salerno, A.: Counting points over finite fields and hypergeometric functions. Funct. Approx. Comment. Math. 49, 137–157 (2013)
Sussman, D.M., Wootters, W.K.: Discrete phase space and minimum-uncertainty states. In: Hirota, O., Shapiro, J.H., Sasaki, M. (eds.) Proceedings of the Eighth International Conference on Quantum Communication, Measurement and Computing, NICT Press (2007). arXiv:0704.1277