Research: Number Theory

Research

Well-rounded forms and the Voronoi tessellation

One identifies the space of binary quadratic forms with the upper half plane $$\mathfrak{h}$$. The set of well-rounded forms corresponds to an…


Hermite Constants for Real Quadratic Fields

The Hermite constant for the ring of integers in real quadratic fields $$\mathbb{Q}(\sqrt{d})$$ for square-free positive integers $$d$$ are plotted above. The…


Extensions of the $$p$$-adic field $$\mathbb{Q}_p$$ with Galois group $$E_1$$

Let $$p$$ be an odd prime number. The graph shows the subgroup lattice of the group $$E_1$$, which is the unique non-abelian…


Congruence Subgroups of $$\textrm{PSL}(2,\mathbb{Z})$$

^ Level 19 Name Index  con  len  c2  c3 > Cusps Gal  Supergroups  Subgroups 19A14 285 1 285 5 6 1915 61  91  1815 19A2…


Involve — a journal of mathematics

The mathematics journal Involve is dedicated to showcasing and encouraging high quality mathematical research involving students (at all levels). The editorial board consists of…


Riemann zeta Function $$\zeta$$ and its Derivative $$\zeta’$$

The absolute value of the Riemann zeta function $$\zeta(\sigma+it)$$ for $$0 \le \sigma \le 8$$ and $$0.1 \le t \le 60$$ over…


Zeros and Zero-Free Regions of $$\zeta^{(38)}$$

The plot shows the distribution of the zeros of the 38th derivative of the Riemann zeta function on the complex plane with…


Zeros of the derivatives of the Riemann zeta function

The plot shows zeros k of the derivatives $$\zeta^{(k)}(\sigma+it)$$ of the Riemann Zeta functionon the complex plane. In 1965 Spira had already…


Zeros of the derivatives of the Riemann zeta function on the left half plane

The plot shows zeros k of the derivatives $$\zeta^{(k)}(\sigma+it)$$ of the Riemann Zeta function the complex plane. For a table of zeros…