Speciality:
01.01.06 (Mathematical logic, algebra, and number theory)
Phone: +61 2 49215530
E-mail: Website: https://wain.mi.ras.ru, https://www.newcastle.edu.au/profile/wadim-zudilin Keywords: irrationality and transcendence problems of mathematical functions and their values,
ordinary and basic hypergeometric series,
arithmetical properties of solutions of differential/difference equations,
multiple zeta values.
UDC: 511.36, 517.53, 517.58, 511.3, 511.334, 517.953, 519.11, 517.5, 517.588, 519.68, 511, 517 MSC: 11J72, 11J81, 11J82, 11F03, 11F11, 11F12, 11F30, 11F46, 33B30, 33C05, 33C20, 33C45, 33C47, 33C50
Subject:
Some results on arithmetical nature of values of Riemann's zeta function at positive integers were obtained; it was proved that at least one of the numbers $\zeta(5),\zeta(7),\zeta(9),\zeta(11)$ is irrational; new continued fractions for Catalan's constant and $\zeta(4)$ were established; estimates for irrationality measures of $q$-analogues of harmonic series, $\log(2)$, and $\zeta(2)$ were obtained; transcendence degree of the differential field generated by Siegel modular forms and exponential functions in arbitrary dimension was obtained (with D. Bertrand); differential equations for thetanulls in arbitrary dimension were discovered; estimates for irrationality and linear independence measures of values of $E$- and $G$-functions were obtained.
Main publications:
W. Zudilin, “Irrationality of values of the Riemann zeta function”, Russian Acad. Sci. Izv. Math., 66:3 (2002), 489–542
W. V. Zudilin, “On the irrationality measure for a $q$-analogue of $\zeta(2)$”, Russian Acad. Sci. Sb. Math., 193:8 (2002), 1151–1172
D. Bertrand, W. Zudilin, “On the transcendence degree of the differential field generated by Siegel modular forms”, J. Reine Angew. Math. (Crelles Journal), 554 (January 2003), 47–68
T. Rivoal, W. Zudilin, “Diophantine properties of numbers related to Catalan's constant”, Math. Ann., 326:4 (2003), 705–721
W. Zudilin, “Arithmetic of linear forms involving odd zeta values”, J. Théorie Nombres Bordeaux, 16:1 (2004), 251–291
W. V. Zudilin, “Well-poised hypergeometric transformations of Euler-type multiple integrals”, J. London Math. Soc. (2), 70:1 (2004), 215–230
