Permission is granted to use these images/animations/sounds in news stories/blog postings concerning the LMFDB.


wavy blue and yellow pattern in a tall rectangle with a curved lower edge

A Maass form, one of the 20 different types of objects in the LMFDB.
Image by Fredrik Strömberg


dark pattern of dots with white ridges curving up in the center, and dim dark bands running horozontally

The zeros of 10,000 different L-functions. The curved white regions (called “sand dunes” by Michael Rubinstein, who discovered them) come from universal properties of the zeros of L-functions. The darker horizontal bands are the shadows of zeros of the Riemann zeta function.
Image by Michael Rubinstein


clusters of pink, white, and blue dots, connected by a network of white lines

The current state of the LMFDB source code.



Listen to the zeta function

The Riemann-Hardy Z-function from 10 to 20,000, interpreted as a sound wave.
MP3 file courtesy of David W. Farmer. Duration: 20 seconds.


graph of a wiggly function, with large negative spikes near 14 and -14

The Z-function of the first rank 4 elliptic curve.
The “fangs” are due to the influence of the zeros of the Riemann zeta function.
Image courtesy of LMFDB.


orange square with green-yellow lines running horizontally,
vertically, and diagonally

The triple correlation of the zeros of the Riemann zeta function.
The stripes are due to the influence of the first few zeros of the Riemann zeta function on the later zeros.
Image courtesy of Nina Snaith.


curved triangles of several colors, tiling the plane

Action of the modular group on the upper half plane.
Image courtesy of Andrew V. Sutherland


Additional pictures available on Alina Bucur’s web page.