New Number Theory Capabilities: New in Mathematica 7

New Number Theory Capabilities

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. »


Compute Dirichlet Character Tables	Visualize Dirichlet L-Functions	Plot Special Sequences

Visualize Prime Related Functions	Sum over Divisors	Compute Dirichlet Transforms

Find Closed Forms for Number Theoretic Sums and Products	Evaluate Ordinary and Exponential Generating Functions	Work with Holonomic Sequences

More About

Prime Numbers

Analytic Number Theory

Multiplicative Number Theory

Additive Number Theory

Arithmetic Functions

q Functions

Discrete Calculus