• Publications
  • Influence
A Survey of Classical Mock Theta Functions
In his last letter to Hardy, Ramanujan defined 17 functions M(q), | q | < 1, which he called mock θ-functions. He observed that as q radially approaches any root of unity ζ at which M(q) has anExpand
  • 89
  • 21
Some Eighth Order Mock Theta Functions
  • 84
  • 14
A search for Fibonacci-Wieferich and Wolstenholme primes
TLDR
We provide statistical data relevant to occurrences of small values of the Fibonacci-Wieferich quotient F p-(p 5) /p modulo p. Expand
  • 48
  • 8
  • PDF
Some Asymptotic Formulae for q-Shifted Factorials
The q-shifted factorial defined by (a : qk)n = (1 − a) (1 − aqk)(1 − aq2k)... (1 − aq(n − 1)k) appears in the terms of basic hypergeometric series. Complete asymptotic expansions as q → 1 of someExpand
  • 32
  • 7
Second Order Mock Theta Functions
Abstract In his last letter to Hardy, Ramanujan defined 17 functions $F\left( q \right)$ , where $\left| q \right|<1$ . He called them mock theta functions, because as $q$ radially approaches anyExpand
  • 51
  • 6
  • PDF
Modular Transformations of Ramanujan's Fifth and Seventh Order Mock Theta Functions
In his last letter to Hardy, Ramanujan defined 17 functions F(q), where |q| < 1. He called them mock theta functions, because as q radially approaches any point e2πir (r rational), there is a thetaExpand
  • 43
  • 5
On the converse of Wolstenholme's Theorem
The problem of distinguishing prime numbers from composite numbers (. . .) is known to be one of the most important and useful in arithmetic. (. . .) The dignity of the science itself seems toExpand
  • 39
  • 4
  • PDF
An Asymptotic Formula for Binomial Sums
Abstract We obtain complete asymptotic expansions for certain binomial sums, including the Apery numbers. In general, binomial sums cannot be expressed by closed formulae, but they do satisfyExpand
  • 20
  • 3
...
1
2
3
...