We show that the v-number of an arbitrary monomial ideal is bounded below by the v-number of its polarization and also find a criteria for the equality. By showing the additivity of associated primes of monomial ideals, ...

In 1914, Hardy proved that infinitely many non-trivial zeros of the Riemann zeta function lie on the critical line using the transformation formula of the Jacobi theta function. Recently the first author obtained an integral ...