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Ramanujan-type supercongruences
Abstract We present several supercongruences that may be viewed as p-adic analogues of Ramanujan-type series for 1 / π and 1 / π 2 , and prove three of these examples.
A q-microscope for supercongruences
Abstract By examining asymptotic behavior of certain infinite basic (q-) hypergeometric sums at roots of unity (that is, at a ‘q-microscopic’ level) we prove polynomial congruences for theirExpand
ZETA STARS
We present two new families of identities for the multiple zeta (star) values: The first one generalizes the formula ζ({2}n , 1) = 2ζ(2n + 1), where {2}n denotes the n-tuple (2, 2, . . . , 2), whileExpand
Tables of Calabi-Yau equations
The main part of this paper is a big table (see Appendix A) containing what we believe to be a complete list of all fourth order equations of Calabi–Yau type known so far. In the text preceding theExpand
From L-series of elliptic curves to Mahler measures
Abstract We prove the conjectural relations between Mahler measures and L-values of elliptic curves of conductors 20 and 24. We also present new hypergeometric expressions for L-values of ellipticExpand
Cyclic q-MZSV sum☆
Abstract We present a family of identities ‘cyclic sum formula’ and ‘sum formula’ for a version of multiple q -zeta star values. We also discuss a problem of q -generalization of shuffle products.
Differential equations, mirror maps and zeta values
The aim of this work is an analytic investigation of differential equations producing mirror maps as well as giving new examples of mirror maps; one of these examples is related to (rationalExpand
Generating functions of Legendre polynomials: A tribute to Fred Brafman
TLDR
A generalisation of Bailey’s identity and its implication to generating functions of Legendre polynomials of the form ∑ n = 0 ∞ u n P n ( x ) z n is presented. Expand
Divergent Ramanujan-type supercongruences
"Divergent" Ramanujan-type series for $1/\pi$ and $1/\pi^2$ provide us with new nice examples of supercongruences of the same kind as those related to the convergent cases. In this paper we manage toExpand
Regulator of modular units and Mahler measures
  • W. Zudilin
  • Mathematics
  • Mathematical Proceedings of the Cambridge…
  • 14 April 2013
Abstract We present a proof of the formula, due to Mellit and Brunault, which evaluates an integral of the regulator of two modular units to the value of the L-series of a modular form of weight 2 atExpand
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