7 papers
Height lower bounds for elements of highly composite rings
Siu Hang Man, Niclas Technau, Martin Widmer +1
Let be the composite field of all number fields of degree at most . In 2001 Bombieri and Zannier proved that has the Northcott property and…
Pythagoras numbers for infinite algebraic fields
Nicolas Daans, Stevan GajoviÄ, Siu Hang Man +1
We prove that the Pythagoras number of the ring of integers of the compositum of all real quadratic fields is infinite. The same holds for certain infinite totally real cyclotomic…
Most totally real fields do not have universal forms or Northcott property
Nicolas Daans, Vitezslav Kala, Siu Hang Man +2
We show that, in the space of all totally real fields equipped with the constructible topology, the set of fields that admit a universal quadratic form, or have the Northcott prope…
Distributions of parity differences and biases in partitions into distinct parts
Siu Hang Man
For a partition , we let , the parity difference of , be the number of odd parts of minus the number of even parts of . We prove for…
An effective version of the Kuznetsov trace formula for GSp(4)
Félicien Comtat, Didier Lesesvre, Siu Hang Man
We develop an explicit version of the Kuznetsov trace formula for GSp(4), relating sums of Fourier coefficients to Kloosterman sums. We study the precise analytic behaviour of both…
Sails for universal quadratic forms
VÃtÄzslav Kala, Siu Hang Man
We establish a new connection between sails, a key notion in the geometric theory of generalised continued fractions, and arithmetic of totally real number fields, specifically, un…