in short intervals
For any sufficiently large real number , the interval contains at least one integer having at most two prime factors .
-adic estimates for exponential sums and the theorem of Chevalley-Warning
Pairs of additive quadratic forms modulo one
Pairs of square-free values of the type ,
We show that there exist infinitely many consecutive square-free numbers of the form , . We also establish an asymptotic formula for the number of such square-free pairs when does not exceed given sufficiently large positive number.
Partitions quadratiques et cyclotomie
Period polynomials and Gauss sums for finite fields
Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory
Petites solutions des congruences
Petits zéros de fonctions L de formes modulaires
Piatetski-Shapiro meets Chebotarev
Let K be a finite Galois extension of the field ℚ of rational numbers. We prove an asymptotic formula for the number of Piatetski-Shapiro primes not exceeding a given quantity for which the associated Frobenius class of automorphisms coincides with any given conjugacy class in the Galois group of K/ℚ. In particular, this shows that there are infinitely many Piatetski-Shapiro primes of the form a² + nb² for any given natural number n.
Piatetski-Shapiro sequences
Picturesque exponential sums. II:
Poincaré series and Kloosterman sums for SL(3, Z)
Poincaré Series for GL (n): Fourier Expansion, Kloosterman Sums, and Algebreo-Geometric Estimates.
Poincaré Series on GL (r) and Kloostermann Sums.
Points rationnels sur les quotients d’Atkin-Lehner de courbes de Shimura de discriminant
Soient et deux nombres premiers distincts et le quotient de la courbe de Shimura de discriminant par l’involution d’Atkin-Lehner . Nous décrivons un moyen permettant de vérifier un critère de Parent et Yafaev en grande généralité pour prouver que si et satisfont des conditions de congruence explicites, connues comme les conditions du cas non ramifié de Ogg, et si est assez grand par rapport à , alors le quotient n’a pas de point rationnel non spécial.
Pointwise ergodic theorems for arithmetic sets
Power-moments of SL Kloosterman sums
Classical Kloosterman sums have a prominent role in the study of automorphic forms on GL and further they have numerous applications in analytic number theory. In recent years, various problems in analytic theory of automorphic forms on GL have been considered, in which analogous GL-Kloosterman sums (related to the corresponding Bruhat decomposition) appear. In this note we investigate the first four power-moments of the Kloosterman sums associated with the group SL. We give formulas for the...
Prime geodesic theorem.
Prime numbers along Rudin–Shapiro sequences
For a large class of digital functions , we estimate the sums (and , where denotes the von Mangoldt function (and the Möbius function). We deduce from these estimates a Prime Number Theorem (and a Möbius randomness principle) for sequences of integers with digit properties including the Rudin-Shapiro sequence and some of its generalizations.