Related papers: On a suspension formula for Denef-Loeser zeta func…
In this paper new classes of $L_2$-orthogonal functions are constructed as iterated $L_2$-orthogonal systems. In order to do this we use the theory of the Riemann's zeta-function as well as our theory of Jacob's ladders. The main result is…
We describe an effective procedure to compute the local subgroup zeta functions of the free class-$2$-nilpotent groups on $d$ generators, for all $d$. For $d=4$, this yields a new, explicit formula. For $d\in\{4,5\}$, we compute the…
Assuming the Riemann Hypothesis we obtain an upper bound for the moments of the Riemann zeta-function on the critical line. Our bound is nearly as sharp as the conjectured asymptotic formulae for these moments. The method extends to moments…
We give a proof the monodromy conjecture relating the poles of motivic zeta functions with roots of b-functions for isolated quasihomogeneous hypersurfaces, and more generally for semi-quasihomogeneous hypersurfaces. We also give a strange…
We associate with an infinite cyclic cover of a punctured neighborhood of a simple normal crossing divisor on a complex quasi-projective manifold (assuming certain finiteness conditions are satisfied) a rational function in $K_0({\rm…
This paper proposes a conjecture on special values of L-functions of geometric motives over Z. This includes L-functions of mixed motives over Q and Hasse-Weil zeta-functions of schemes over Z. We conjecture the following: the order of L(M,…
We extend the approach Abbott, Kedlaya and Roe to computation of the zeta function of a projective hypersurface with $\tau$ isolated ordinary double points over a finite field $\mathbb{F}_q$ given by the reduction of a homogeneous…
We use the Arakawa-Berndt theory of generalized eta-functions to prove a conjecture of Lal\`in, Rodrigue and Rogers concerning the algebraic nature of special values of the secant zeta functions.
This paper discuss a new class of functional equations by using both Poisson summation formula and Jacobi type theta a function. The class of Riemann type functional equations are derived from self-reciprocal probability density functions.…
A characterization of dynamically defined zeta functions is presented. It comprises a list of axioms, natural extension of the one which characterizes topological degree, and a uniqueness theorem. Lefschetz zeta function is the main (and…
Associated to classical semi-simple groups and their maximal parabolics are genuine zeta functions. Naturally related to Riemann's zeta and governed by symmetries, including that of Weyl, these zetas are expected to satisfy the Riemann…
We use a formula of Bultot to compute the motivic zeta function for the toric degeneration of the quartic K3 and its Gross-Siebert mirror dual degeneration. We check for this explicit example that the identification of the logarithm of the…
The global additive and multiplicative properties of the Laplacian on j-forms and related zeta functions are analyzed. The explicit form of zeta functions on a product of closed oriented hyperbolic manifolds \Gamma\backslash{\Bbb H}^d and…
New recursion relations for the Riemann zeta function are introduced. Their derivation started from the standard functional equation. The new functional equations have both real and imaginary increment versions and can be applied over the…
Our understanding of local index formula in noncommutative geometry is stalled for a while because we do not have more than one explicit computation, namely that of Connes for quantum SU(2) and do not understand the meaning of the various…
In this note, we give a formula for the Whittaker-Shintani functions for the p-adic symplectic groups, which is a generalization of the Zonal spherical functions and Whittaker functions. We then use the formula to give an alternative proof…
Based on the theory of rigid cohomology, we provide an explicit formula of zeta functions of certain K3 families, which we call the hypergeometric type. The central point of our argument is the comparison between the 2nd rigid cohomology of…
We show that the notion of zeta functions over F1, as given in special cases by Soule', extends naturally to all F1-schemes as defined earlier by the author. We further give two constructions of K-theory for affine schemes or F1-rings, we…
The secondary zeta function is defined as a generalized zeta series over the imaginary parts of non-trivial zeros assuming (RH). This function admits Laurent series expansion at the double pole at $s=1$. In this article, we derive a new…
We prove the local motivic monodromy conjecture for singularities that are nondegenerate with respect to a simplicial Newton polyhedron. It follows that all poles of the local topological zeta functions of such singularities correspond to…