Some wonderful formulae... Footnotes to Apery’s proof of the irrationality of
Some youthful ways to evaluate .
Some -results related to the fourth power moment of the Riemann zeta-function and to the additive divisor problem
We improve the “two-sided” omega results in the fourth power mean problem for the Riemann zeta-function and in the additive divisor problem.
Some Ω-theorems for the Riemann zeta-function
Sommes de Dedekind elliptiques et formes de Jacobi
À partir des formes de Jacobi , on construit une somme de Dedekind elliptique. On obtient ainsi un analogue elliptique aux sommes multiples de Dedekind construites à partir des fonctions cotangentes, étudiées par D. Zagier. En outre, on établit une loi de réciprocité satisfaite par ces nouvelles sommes. Par une procédure de limite, on peut retrouver la loi de réciprocité remplie par les sommes multiples de Dedekind classiques. D’autre part, en les spécialisant en des paramètres de points de 2- division,...
Spacing of zeros of Hecke L-functions and the class number problem
Special values of multiple gamma functions
We give a Chowla-Selberg type formula that connects a generalization of the eta-function to with multiple gamma functions. We also present some simple infinite product identities for certain special values of the multiple gamma function.
Spectral statistics.
Square-full divisors of square-full integers.
Standard Models of Abstract Intersection Theory for Operators in Hilbert Space
For an operator in a possibly infinite-dimensional Hilbert space of a certain class, we set down axioms of an abstract intersection theory, from which the Riemann hypothesis regarding the spectrum of that operator follows. In our previous paper (2011) we constructed a GNS (Gelfand-Naimark-Segal) model of abstract intersection theory. In this paper we propose another model, which we call a standard model of abstract intersection theory. We show that there is a standard model of abstract intersection...
Standard relations of multiple polylogarithm values at roots of unity.
Statistical Deuring-Heilbronn phenomenon
Strong spectral gaps for compact quotients of products of )
The existence of a strong spectral gap for quotients of noncompact connected semisimple Lie groups is crucial in many applications. For congruence lattices there are uniform and very good bounds for the spectral gap coming from the known bounds towards the Ramanujan–Selberg conjectures. If has no compact factors then for general lattices a spectral gap can still be established, but there is no uniformity and no effective bounds are known. This note is concerned with the spectral gap for an irreducible...
Subconvexity for the Riemann zeta-function and the divisor problem
Subgroups of finite index in nilpotent groups.
Summation formulae and their relation to Dirichlet's series
Summation operators and "explicit formulas"
Sums of coefficients of Hecke series
Sums of L-functions over rational function fields
Sums of some multiplicative functions over a special set of integers