Some Remarks on Landau-siegel Zeros

On the Landau-Siegel Zeros Conjecture

Landau-siegel Zeros and Zeros of the Derivative of the Riemann Zeta Function

We show that if the derivative of the Riemann zeta function has sufficiently many zeros close to the critical line, then the zeta function has many closely spaced zeros. This gives a condition on the zeros of the derivative of the zeta function which implies a lower bound of the class numbers of imaginary quadratic fields.

Landau-Siegel Zeroes and Black Hole Entropy

In [1] some connections were made between string theoretic models of black holes and certain issues in arithmetic. One of the more speculative suggestions in [1] was a proposal that the entropy of BPS black holes is related to an arithmetic height of certain arithmetic varieties. In the present note we remark on some connections between these speculations and some issues related to the Riemann ...

Some Siegel threefolds with a Calabi-Yau model

2009 Introduction In the following we describe some examples of Calabi-Yau manifolds that arise as desingularizations of certain Siegel threefolds. Here by a Calabi-Yau mani-fold we understand a smooth complex projective variety which admits a holo-morphic differential form of degree three without zeros and such that the first Betti number is zero. This differential form is unique up to a const...

Exact solutions of the 2D Ginzburg-Landau equation by the first integral method

The first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to non integrable equations as well as to integrable ones. In this paper, the first integral method is used to construct exact solutions of the 2D Ginzburg-Landau equation.