186 papers
This paper presents a method to guarantee that the Jacobian of a smooth curve has a strictly positive Mordell-Weil rank by proving that such a rank exists whenever the curve possesses a rational degree 1 divisor class but lacks rational non-trivial 2-torsion and rational theta characteristics.
This paper investigates and compares the properties of q-Narayana polynomials specifically at the values and .
This paper demonstrates that, contrary to the classical Grunwald–Wang theorem's special case where the obstruction is a group of order 2, the obstruction in the generalized setting for valued fields is not always finite nor bounded independently of the number of places, even for rational function fields.
This paper proves that for sufficiently large integers satisfying specific modular constraints, can be expressed as the sum of four generalized polygonal numbers whose parameters have at most 988 prime factors.
This paper proves that symmetric formal Fourier-Jacobi series of Hermitian modular forms over arbitrary imaginary quadratic fields converge to genuine modular forms, thereby establishing the geometric unitary Kudla conjecture in arbitrary codimension and removing the modularity hypothesis from the arithmetic inner product formula of Li-Liu.
This paper introduces the concept of abelian-normal numbers by adapting abelian complexity functions to digit expansions, constructs a non-normal analogue of Champernowne's constant that satisfies this new property, and proposes open problems regarding its behavior.