Large deviations of Montgomery type and its application to the theory of zeta-functions
Large deviations of sums of independent random variables
Large gaps between consecutive zeros of the Riemann zeta-function. II
Assuming the Riemann Hypothesis we show that there exist infinitely many consecutive zeros of the Riemann zeta-function whose gaps are greater than 2.9 times the average spacing.
Large values of certain number-theoretic error terms
Large values of Dirichlet polynomials
Large Values of the Error Term in the Divisor Problem.
Laurent Expansion of Dirichlet Series-II.
Limit theorem in the space of continuous functions for the Dirichlet polynomial related with the Riemann zeta-funtion
A limit theorem in the space of continuous functions for the Dirichlet polynomialwhere denote the coefficients of the Dirichlet series expansion of the function in the half-plane
Limit theorems for the Mellin transform of the square of the Riemann zeta-function. I
Logarithmic derivative of the Euler Γ function in Clifford analysis.
The logarithmic derivative of the Γ-function, namely the ψ-function, has numerous applications. We define analogous functions in a four dimensional space. We cut lattices and obtain Clifford-valued functions. These functions are holomorphic cliffordian and have similar properties as the ψ-function. These new functions show links between well-known constants: the Eurler gamma constant and some generalisations, ζR(2), ζR(3). We get also the Riemann zeta function and the Epstein zeta functions.
Lower bounds for power moments of L-functions
Lower bounds for relative class numbers of imaginary abelian number fields and CM-fields
Lower bounds of discrete moments of the derivatives of the Riemann zeta-function on the critical line
We establish unconditional lower bounds for certain discrete moments of the Riemann zeta-function and its derivatives on the critical line. We use these discrete moments to give unconditional lower bounds for the continuous moments , where is a non-negative integer and a rational number. In particular, these lower bounds are of the expected order of magnitude for .
Lower order terms of the second moment of S(t)