With the continued advance of computing power and accessibility, the view that" real
mathematicians don't compute" no longer has any traction for a newer generation of …

Ramanujan-type supercongruences Page 1 arXiv:0805.2788v3 [math.NT] 14 Oct 2008
RAMANUJAN-TYPE SUPERCONGRUENCES WADIM ZUDILIN Abstract. We present several …

When we pause to reflect on Ramanujan's life, we see that there were certain events that
seemingly were necessary in order that Ramanujan and his mathematics be brought to …

We give a systematic treatment of lattice Green's functions (LGF) on the d-dimensional
diamond, simple cubic, body-centred cubic and face-centred cubic lattices for arbitrary …

361 Rational analogues of Ramanujan’s series for 1/π† Page 1 Math. Proc. Camb. Phil. Soc.
(2012), 153, 361–383 c Cambridge Philosophical Society 2012 doi:10.1017/S0305004112000254 …

We prove the last remaining case of the original 13 Ramanujan-type supercongruence
conjectures due to Van Hamme from 1997. The proof utilizes classical congruences and a …

EISENSTEIN SERIES AND RAMANUJAN-TYPE SERIES FOR 1/π 1. Introduction In his famous
paper [37], [38, pp. 36–38], Ramanujan reco Page 1 EISENSTEIN SERIES AND …

The modified Abel lemma on summation by parts is employed to investigate the partial sum
of Dougall's $ _5H_5 $-series. Several unusual transformation formulae into fast convergent …

There are many instances known when the Fourier coefficients of modular forms are
congruent to partial sums of hypergeometric series. In our previous work, such partial sums …

The main goal of this survey is to give common characteristics of auxiliary hypergeometric
functions (and their generalisations), functions which occur in number-theoretic problems …