Tapani Matala-aho

An application of Jacobi type polynomials to irrationality measures

The paper provides irrationality measures for certain values of binomial functions and definite integrals of some rational functions. The results are obtained using Jacobi type polynomials and divisibility considerations of their coefficients.

New irrationality measures for q-logarithms

The three main methods used in diophantine analysis of q-series are combined to obtain new upper bounds for irrationality measures of the values of the q-logarithm function when p = 1/q ∈ Z \ {0, ±1} and z ∈ Q.

ON IRRATIONALITY MEASURES OF THE VALUES OF GAUSS HYPERGEOMETRIC FUNCTION

The paper gives irrationality measures for the values of some Gauss hypergeometric functions both in the archimedean andp-adic case. Further, an improvement of general results is obtained in the case of logarithmic function.

On Diophantine Approximations of Mock Theta Functions of Third Order

The paper gives bounds for the approximation of the values of Ramanujans Mock Theta functions of third order and more generally of some q-hypergeometric functions by the elements of an algebraic number field. Simultaneous approximations for the values of q-exponential function are also obtained. All the results are given both in the archimedean and p-adic case.

On Diophantine approximations of the solutions of q-functional equations

Rn = Pn;1 ¬ 1 + ¢ ¢ ¢+ Pn;m ¬ m ; Pn;1 ; : : : ; Pn;m 2 K; n 2 N; in m > 2 complex or p-adic numbers ¬ 1 ; : : : ; ¬ m 2 Kv with appropriate growth conditions, Nesterenko proved a lower bound for the dimension d of the vector space K¬ 1 + ¢ ¢ ¢+ K ¬ m over K, when K = Q and v is the in nite place. We shall generalize Nesterenko’ s dimension estimate over number elds K with appropriate places v, if the lower bound condition for jRn j is replaced by the determinant condition. For the q-series approximations also a linear independence measure is given for the d linearly independent numbers. As an application we prove that the initial values F (t); F (qt); : : : ; F (q i t) of the linear homogeneous q-functional equation NF (q t) = P1F (q m i 1 t) + P2F (q m i t) + ¢ ¢ ¢+ PmF (t); where N = N (q; t), Pi = Pi(q; t) 2 K[q; t] (i = 1; : : : ; m), generate a vector space of dimension d > 2 over K under some conditions for the coe± cient polynomials, the solution F (t) and t; q 2 K¤.

An explicit Baker-type lower bound of exponential values

Let

On Baker type lower bounds for linear forms

\mathbb{I}

Continued fractional measure of irrationality

denote an imaginary quadratic field or the field

ON THE VALUES OF CONTINUED FRACTIONS: q-SERIES II

\mathbb{Q}

On Mahler’s Transcendence Measure for e

of rational numbers and