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For more than 20 years, Mathematica has been steadily expanding the domain of numeric and symbolic computational number theory, taking theoretical constructs, and implementing them in a convenient and consistent computational form. Mathematica 7 introduces a broad range of new capabilities of importance across analytic, multiplicative and additive number theory.
- Explicit computation and symbolic manipulation of Dirichlet characters and Dirichlet L-functions. »
- General symbolic representation of sums over divisors. »
- Dirichlet transform and convolution. »
- Greatly extended evaluation of number theoretic sums and products.
- Comprehensive support for q-functions and q-series. »
- (n), (n), Mangoldt lambda, Liouville lambda and other functions in arithmetic number theory. »
- Prime zeta function and Riemann prime counting function. »
- Systematic computation with holonomic sequences.
- Support for ordinary and exponential generating functions. »
- Extensive support for integer sequence recognition. »
- New discrete sequence visualization function. »