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Modular functions and transcendence questions

- Y. Nesterenko
- Mathematics
- 31 October 1996

We prove results on the transcendence degree of a field generated by numbers connected with the modular function . In particular, we show that and are algebraically independent and we prove… Expand

Integral identities and constructions of approximations to zeta-values

- Y. Nesterenko
- Mathematics
- 2003

Nous presentons une construction generale de combinaisons lineaires a coefficients rationnels en les valeurs de la fonction zeta de Riemann aux entiers. Ces formes lineaires sont exprimees en termes… Expand

Linear independence of values of E-functions

- Y. Nesterenko, A. B. Shidlovskii
- Mathematics
- 31 August 1996

We prove a general theorem that establishes a relation between linear and algebraic independence of values at algebraic points of E-functions and properties of the ideal formed by all algebraic… Expand

A few remarks on ζ(3)

- Y. Nesterenko
- Mathematics
- 1 June 1996

A new proof of the irrationality of the number ζ(3) is proposed. A new decomposition of this number into a continued fraction is found. Recurrence relations are proved for some sequences of… Expand

On an equation of Goormaghtigh

- Y. Nesterenko, T. N. Shorey
- Mathematics
- 1998

Nagell [5] confirmed a conjecture of Ramanujan [6] that the solutions of equation x + 7 = 2 in integers x > 0, n > 0 are given by (x, n) = (1, 3), (3, 4), (5, 5), (11, 7), (181, 15). This result… Expand

Perfect powers in products of integers from a block of consecutive integers (II)

- T. N. Shorey, Y. Nesterenko
- Mathematics
- 1987

(1) (m+ d1) . . . (m+ dt) = by in m, t, d1, . . . , dt, b, y and l. We always assume that the left hand side of equation (1) is divisible by a prime exceeding k. Consequently, there is an i with 1 ≤… Expand

ESTIMATES FOR THE CHARACTERISTIC FUNCTION OF A PRIME IDEAL

- Y. Nesterenko
- Mathematics
- 28 February 1985

Let be a field of characteristic 0, a homogeneous prime ideal of the ring () and the set of residues of homogeneous polynomials of degree ( is a natural number) in , taken modulo . In this paper an… Expand

New Advances in Transcendence Theory: Estimates for the number of zeros of certain functions

- Y. Nesterenko
- Mathematics
- 1988

On the irrationality exponent of the number ln 2

- Y. Nesterenko
- Mathematics
- 9 November 2010

We propose another method of deriving the Marcovecchio estimate for the irrationality measure of the number ln 2 following, for the most part, the method of proof of the irrationality of the number… Expand

ON ALGEBRAIC INDEPENDENCE OF ALGEBRAIC POWERS OF ALGEBRAIC NUMBERS

- Y. Nesterenko
- Mathematics, Computer Science
- 28 February 1985

It is proved that among the numbers , where is algebraic, , and is algebraic of degree , there are no fewer than which are algebraically independent over .Bibliography: 17 titles.

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