Low-Discrepancy Point Sets.
Low-discrepancy point sets for non-uniform measures
We prove several results concerning the existence of low-discrepancy point sets with respect to an arbitrary non-uniform measure μ on the d-dimensional unit cube. We improve a theorem of Beck, by showing that for any d ≥ 1, N ≥ 1, and any non-negative, normalized Borel measure μ on there exists a point set whose star-discrepancy with respect to μ is of order . For the proof we use a theorem of Banaszczyk concerning the balancing of vectors, which implies an upper bound for the linear discrepancy...
Low-discrepancy point sets obtained by digital constructions over finite fields
Low-discrepancy sequences obtained from algebraic function fields over finite fields
Low-discrepancy sequences using duality and global function fields
Lower and upper bounds for the number of solutions of
Lower and upper bounds for the splitting of separatrices of a pendulum under a fast quasiperiodic forcing.
Lower Bound for a Diophantine Approximation Function.
Lower bound for class numbers of certain real quadratic fields
Let be a square-free positive integer and be the class number of the real quadratic field We give an explicit lower bound for , where . Ankeny and Chowla proved that if is a natural number and is a square-free integer, then whenever . Applying our lower bounds, we show that there does not exist any natural number such that . We also obtain a similar result for the family . As another application, we deduce some criteria for a class group of prime power order to be cyclic.
Lower bound of real primitive L-function at s=1
Lower bounds for a certain class of error functions
Lower bounds for a conjecture of Erdős and Turán
We study representation functions of asymptotic additive bases and more general subsets of ℕ (sets with few nonrepresentable numbers). We prove that if ℕ∖(A+A) has sufficiently small upper density (as in the case of asymptotic bases) then there are infinitely many numbers with more than five representations in A+A, counting order.
Lower bounds for discriminants of number fields
Lower bounds for expressions of large sieve type
We show that the large sieve is optimal for almost all exponential sums.
Lower Bounds for Heights on Finitely Generated Groups.
Lower bounds for perfect rational cuboids
Lower bounds for power moments of L-functions
Lower bounds for relative class numbers of imaginary abelian number fields and CM-fields
Lower bounds for resultants, I
Lower bounds for simultaneous Diophantine approximation constants
After a brief exposition of the state-of-art of research on the (Euclidean) simultaneous Diophantine approximation constants , new lower bounds are deduced for and .