Roberto Tauraso

New congruences for central binomial coefficients

Let p be a prime and let a be a positive integer. In this paper we determine

ON SOME NEW CONGRUENCES FOR BINOMIAL COEFFICIENTS

\sum_{k=0}^{p^a-1}\binom{2k}{k+d}/m^k

New properties of multiple harmonic sums modulo p and p-analogues of Leshchiner’s series

and

Rigidity at the boundary for holomorphic self-maps of the unit disk

\sum_{k=1}^{p-1}\binom{2k}{k+d}/(km^{k-1})

Identity principles for commuting holomorphic self-maps of the unit disc

modulo

Commuting holomorphic maps of the unit disc

p

CONGRUENCES CONCERNING JACOBI POLYNOMIALS AND APÉRY-LIKE FORMULAE

for all d=0,...,p^a, where m is any integer not divisible by p. For example, we show that if

The Lindelof principle and angular derivatives in convex domains of finite type

p\not=2,5

Supercongruences related to 3F2(1) involving harmonic numbers

then