Varchenko, Alexander On the number of \(p\)-hypergeometric solutions of KZ equations. (English) Zbl 1523.32025 Ramanujan J. 62, No. 1, 307-327 (2023). Reviewer: Dmitry Artamonov (Moskva) MSC: 32G34 33C60 33E50 PDFBibTeX XMLCite \textit{A. Varchenko}, Ramanujan J. 62, No. 1, 307--327 (2023; Zbl 1523.32025) Full Text: DOI arXiv
Varchenko, Alexander [Sperber, Steven] Notes on solutions of KZ equations modulo \(p^s\) and \(p\)-adic limit \(s\to\infty\). (English) Zbl 1497.13020 Koelink, Erik (ed.) et al., Hypergeometry, integrability and Lie theory. Virtual conference, Lorentz Center, Leiden, the Netherlands, December 7–11, 2020. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 780, 309-347 (2022). MSC: 13A35 11G25 14G10 33C60 32G20 PDFBibTeX XMLCite \textit{A. Varchenko}, Contemp. Math. 780, 309--347 (2022; Zbl 1497.13020) Full Text: DOI arXiv
Varchenko, Alexander Determinant of \(\mathbb{F}_p\)-hypergeometric solutions under ample reduction. (English) Zbl 1497.13019 Koelink, Erik (ed.) et al., Hypergeometry, integrability and Lie theory. Virtual conference, Lorentz Center, Leiden, the Netherlands, December 7–11, 2020. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 780, 287-307 (2022). MSC: 13A35 33C60 32G20 PDFBibTeX XMLCite \textit{A. Varchenko}, Contemp. Math. 780, 287--307 (2022; Zbl 1497.13019) Full Text: DOI arXiv
Rimányi, Richárd; Varchenko, Alexander The \({{\mathbb{F}}}_p\)-Selberg integral. (English) Zbl 1496.13008 Arnold Math. J. 8, No. 1, 39-60 (2022). Reviewer: Janet Vassilev (Albuquerque) MSC: 13A35 33C60 32G20 PDFBibTeX XMLCite \textit{R. Rimányi} and \textit{A. Varchenko}, Arnold Math. J. 8, No. 1, 39--60 (2022; Zbl 1496.13008) Full Text: DOI arXiv
Slinkin, Alexey; Varchenko, Alexander Hypergeometric integrals modulo \(p\) and Hasse-Witt matrices. (English) Zbl 1477.13016 Arnold Math. J. 7, No. 2, 267-311 (2021). Reviewer: Ahmed Lesfari (El Jadida) MSC: 13A35 33C60 32G20 PDFBibTeX XMLCite \textit{A. Slinkin} and \textit{A. Varchenko}, Arnold Math. J. 7, No. 2, 267--311 (2021; Zbl 1477.13016) Full Text: DOI arXiv
Rimányi, Richárd; Varchenko, Alexander The \(\mathbb{F}_p\)-Selberg integral of type \(A_n\). (English) Zbl 1487.33018 Lett. Math. Phys. 111, No. 3, Paper No. 71, 24 p. (2021). Reviewer: Vijay Yadav (Virar) MSC: 33E50 13A35 33C60 32G20 PDFBibTeX XMLCite \textit{R. Rimányi} and \textit{A. Varchenko}, Lett. Math. Phys. 111, No. 3, Paper No. 71, 24 p. (2021; Zbl 1487.33018) Full Text: DOI arXiv
Varchenko, Alexander Hyperelliptic integrals modulo \(p\) and Cartier-Manin matrices. (English) Zbl 1456.14036 Pure Appl. Math. Q. 16, No. 3, 315-336 (2020). MSC: 14H25 13A35 32G20 33C60 PDFBibTeX XMLCite \textit{A. Varchenko}, Pure Appl. Math. Q. 16, No. 3, 315--336 (2020; Zbl 1456.14036) Full Text: DOI arXiv
Varchenko, Alexander Solutions modulo \(p\) of Gauss-Manin differential equations for multidimensional hypergeometric integrals and associated Bethe ansatz. (English) Zbl 1406.33013 Mathematics 5, No. 4, Paper No. 52, 18 p. (2017). MSC: 33C60 17B80 05E10 82B30 PDFBibTeX XMLCite \textit{A. Varchenko}, Mathematics 5, No. 4, Paper No. 52, 18 p. (2017; Zbl 1406.33013) Full Text: DOI arXiv
Varchenko, A. Critical set of the master function and characteristic variety of the associated Gauss-Manin differential equations. (English) Zbl 1323.32024 Arnold Math. J. 1, No. 3, 253-282 (2015). MSC: 32W50 32S40 33C60 PDFBibTeX XMLCite \textit{A. Varchenko}, Arnold Math. J. 1, No. 3, 253--282 (2015; Zbl 1323.32024) Full Text: DOI arXiv
Tarasov, V.; Varchenko, A. Identities between \(q\)-hypergeometric and hypergeometric integrals of different dimensions. (English) Zbl 1113.33015 Adv. Math. 191, No. 1, 29-45 (2005). Reviewer: Valentina Golubeva (Moskva) MSC: 33C60 PDFBibTeX XMLCite \textit{V. Tarasov} and \textit{A. Varchenko}, Adv. Math. 191, No. 1, 29--45 (2005; Zbl 1113.33015) Full Text: DOI arXiv
Varchenko, Alexandre Multidimensional hypergeometric functions in conformal field theory, algebraic \(K\)-theory, algebraic geometry. (English) Zbl 0747.33002 Proc. Int. Congr. Math., Kyoto/Japan 1990, Vol. I, 281-300 (1991). Reviewer: A.Kaneko (Komaba) MSC: 33-02 33C20 33C60 33D80 32S40 14G10 52C35 81T40 PDFBibTeX XMLCite \textit{A. Varchenko}, in: Proceedings of the international congress of mathematicians (ICM), August 21--29, 1990, Kyoto, Japan. Volume I. Tokyo etc.: Springer-Verlag. 281--300 (1991; Zbl 0747.33002)
Varchenko, A. N. The Euler beta-function, the Vandermonde determinant, the Legendre equation and critical values of linear functions on a configuration of hyperplanes. II. (Russian) Zbl 0699.33004 Izv. Akad. Nauk SSSR, Ser. Mat. 54, No. 1, 146-158 (1990). Reviewer: A.Kaneko MSC: 33C60 33B15 PDFBibTeX XMLCite \textit{A. N. Varchenko}, Izv. Akad. Nauk SSSR, Ser. Mat. 54, No. 1, 146--158 (1990; Zbl 0699.33004)
Varchenko, A. N. The determinant of the matrix of multidimensional hypergeometric integrals. (English. Russian original) Zbl 0737.05033 Sov. Math., Dokl. 40, No. 2, 359-362 (1990); translation from Dokl. Akad. Nauk SSSR 308, No. 4, 777-780 (1989). MSC: 05B30 15A15 33C60 52B05 PDFBibTeX XMLCite \textit{A. N. Varchenko}, Sov. Math., Dokl. 40, No. 2, 359--362 (1989; Zbl 0737.05033); translation from Dokl. Akad. Nauk SSSR 308, No. 4, 777--780 (1989)
Varchenko, A. N. The Euler beta-function, the Vandermonde determinant, the Legendre equation, and critical values of linear functions on a configuration of hyperplanes. I. (Russian) Zbl 0695.33004 Izv. Akad. Nauk SSSR, Ser. Mat. 53, No. 6, 1206-1235 (1989). Reviewer: A.Kaneko MSC: 33C60 33B15 PDFBibTeX XMLCite \textit{A. N. Varchenko}, Izv. Akad. Nauk SSSR, Ser. Mat. 53, No. 6, 1206--1235 (1989; Zbl 0695.33004)