On the mean square value of Dirichlet’s -functions
On the mean squared modulus of a Dirichlet L-function over a short segment of the critical line
On the mean value of a kind of zeta functions
On the Mean Value of Dirichlet Series.
On the mean value of L(m,χ )L(n,χ̅) at positive integers m,n ≥ 1
On the mean value of the generalized Dirichlet -functions
Let be an integer, let denote a Dirichlet character modulo For any real number we define the generalized Dirichlet -functions where with and both real. They can be extended to all by analytic continuation. In this paper we study the mean value properties of the generalized Dirichlet -functions especially for and , and obtain two sharp asymptotic formulas by using the analytic method and the theory of van der Corput.
On the mean value of the remainder term of the prime number formula
On the method of exponent pairs
On the moderate growth of generalized Dirichlet series for hypoelliptic polynomials
On the modulus of the Riemann zeta function in the critical strip
On the (non-)contractibility of the order complex of the coset poset of an alternating group
On the order of vanishing of modular -functions at the critical point
On the order of
On the orthogonal symmetry of L-functions of a family of Hecke Grössencharacters
The family of symmetric powers of an L-function associated with an elliptic curve with complex multiplication has received much attention from algebraic, automorphic and p-adic points of view. Here we examine one explicit such family from the perspectives of classical analytic number theory and random matrix theory, especially focusing on evidence for the symmetry type of the family. In particular, we investigate the values at the central point and give evidence that this family can be modeled by...
On the problem
On the pair correlation conjecture for zeros of the Riemann zeta-function.
On the papers of Ramachandra and Kátai
On the Partial Fraction Expansion for 0 (x).
On the periodicity of trigonometric functions generalized to quotient rings of R[x]
We apply a method of Euler to algebraic extensions of sets of numbers with compound additive inverse which can be seen as quotient rings of R[x]. This allows us to evaluate a generalization of Riemann’s zeta function in terms of the period of a function which generalizes the function sin z. It follows that the functions generalizing the trigonometric functions on these sets of numbers are not periodic.
On the Periods of Modular Forms.