Scalar product of Dirichlet series and the distribution of integer points on toric varieties.
Second moments of Dirichlet -functions weighted by Kloosterman sums
For the general modulo and a general multiplicative character modulo , the upper bound estimate of is a very complex and difficult problem. In most cases, the Weil type bound for is valid, but there are some counterexamples. Although the value distribution of is very complicated, it also exhibits many good distribution properties in some number theory problems. The main purpose of this paper is using the estimate for -th Kloosterman sums and analytic method to study the asymptotic properties...
Second moments of holomorphic Hilbert modular forms and subconvexity
Selberg Zeta function on an exceptional domain.
Selberg zeta functions associated with a theta multiplier system of SL2(Z) and Jacobi forms.
Series containing the Hurwitz function
Séries de Dirichlet
Séries de Dirichlet associées à des fractions rationnelles de plusieurs variables
Séries hypergéométriques et irrationalité des valeurs de la fonction zêta de Riemann
Nous effectuons un survol des résultats connus sur la nature diophantienne des valeurs de la fonction zêta de Riemann aux entiers. Nous mettons en particulier l’accent sur le rôle important des séries hypergéométriques dans les démonstrations de l’irrationalité de et d’une infinité des nombres .
Séries hypergéométriques multiples et polyzêtas
Nous décrivons un algorithme théorique et effectif permettant de démontrer que des séries et intégrales hypergéométriques multiples relativement générales se décomposent en combinaisons linéaires à coefficients rationnels de polyzêtas.
Sharp bounds for the intersection of nodal lines with certain curves
Let be a hyperbolic surface and let be a Laplacian eigenfunction having eigenvalue with . Let be the set of nodal lines of . For a fixed analytic curve of finite length, we study the number of intersections between and in terms of . When is compact and a geodesic circle, or when has finite volume and is a closed horocycle, we prove that is “good” in the sense of [TZ]. As a result, we obtain that the number of intersections between and is . This bound is sharp.
Siegel zeros of Eisenstein series
Sieve methods and class-number probelms. II.
Sieve methods and class-number problems III.
Sign changes of certain arithmetical function at prime powers
We examine an arithmetical function defined by recursion relations on the sequence and obtain sufficient condition(s) for the sequence to change sign infinitely often. As an application we give criteria for infinitely many sign changes of Chebyshev polynomials and that of sequence formed by the Fourier coefficients of a cusp form.
Sign-changes of the Thue-Morse Fractal Function and Dirichlet L-Series.
Simple zeros of degree 2 -functions
We prove that the complete -functions of classical holomorphic newforms have infinitely many simple zeros.
Simple zeros of the Ramanujan ...-Dirichlet series.
Simple zeros of the zeta function of a quadratic number field. I.
Simultaneous generation of Koecher and Almkvist-Granville's Apéry-like formulae.