Infinite series identities from modular transformation formulas that stem from generalized Eisenstein series
Integral Representations of the Logarithmic Derivative of the Selberg Zeta Function
AMS Subj. Classification: MSC2010: 11F72, 11M36, 58J37We point out the importance of the integral representations of the logarithmic derivative of the Selberg zeta function valid up to the critical line, i.e. in the region that includes the right half of the critical strip, where the Euler product definition of the Selberg zeta function does not hold. Most recent applications to the behavior of the Selberg zeta functions associated to a degenerating sequence of finite volume, hyperbolic manifolds of...
Li coefficients for automorphic -functions
Xian-Jin Li gave a criterion for the Riemann hypothesis in terms of the positivity of a set of coefficients
Local L-factors of motives and regularized determinants.
Meromorphic extensions of generalised zeta functions.
Multiple finite Riemann zeta functions
Non-abelian -adic -functions and Eisenstein series of unitary groups – The CM method
In this work we prove various cases of the so-called “torsion congruences” between abelian -adic -functions that are related to automorphic representations of definite unitary groups. These congruences play a central role in the non-commutative Iwasawa theory as it became clear in the works of Kakde, Ritter and Weiss on the non-abelian Main Conjecture for the Tate motive. We tackle these congruences for a general definite unitary group of variables and we obtain more explicit results in the...
On Eisenstein series with characters and Dedekind sums
On families of counting functions of number fields and hyperbolic manifolds of dimensions two and three
On pairs of closed geodesics on hyperbolic surfaces
In this article we prove a trace formula for double sums over totally hyperbolic Fuchsian groups . This links the intersection angles and common perpendiculars of pairs of closed geodesics on with the inner products of squares of absolute values of eigenfunctions of the hyperbolic laplacian . We then extract quantitative results about the intersection angles and common perpendiculars of these geodesics both on average and individually.
On the ...-factor attached to motives.
On the representation of H-invariants in the Selberg class
On theta type functions associated with the zeros of the Selberg zeta functions.
On zeros of approximate functions of the Rankin-Selberg L-functions
Prime geodesic theorem.
Problems and results on αp - βq
Relative zeta determinants and the geometry of the determinant line bundle.
Remarks on Weil’s quadratic functional in the theory of prime numbers, I
This Memoir studies Weil’s well-known Explicit Formula in the theory of prime numbers and its associated quadratic functional, which is positive semidefinite if and only if the Riemann Hypothesis is true. We prove that this quadratic functional attains its minimum in the unit ball of the -space of functions with support in a given interval , and prove again Yoshida’s theorem that it is positive definite if is sufficiently small. The Fourier transform of the functional gives rise to a quadratic...
Selberg Zeta function on an exceptional domain.
Selberg zeta functions associated with a theta multiplier system of SL2(Z) and Jacobi forms.