scholarly journals The Divisor Function in Arithmetic Progressions to Smooth Moduli

2014 ◽  
Vol 2015 (15) ◽  
pp. 6675-6698 ◽  
Author(s):  
Alastair James Irving
2014 ◽  
Vol 89 (4) ◽  
pp. 979-1014 ◽  
Author(s):  
Étienne Fouvry ◽  
Satadal Ganguly ◽  
Emmanuel Kowalski ◽  
Philippe Michel

2012 ◽  
Vol 153 (3) ◽  
pp. 419-455 ◽  
Author(s):  
PIERRE LE BOUDEC

AbstractWe establish Manin's conjecture for a cubic surface split over ℚ and whose singularity type is 2A2 + A1. For this, we make use of a deep result about the equidistribution of the values of a certain restricted divisor function in three variables in arithmetic progressions. This result is due to Friedlander and Iwaniec (and was later improved by Heath–Brown) and draws on the work of Deligne.


2018 ◽  
Vol 30 (2) ◽  
pp. 269-293
Author(s):  
Brad Rodgers ◽  
Kannan Soundararajan

AbstractWe study the variance of sums of thek-fold divisor function{d_{k}(n)}over sparse arithmetic progressions, with averaging over both residue classes and moduli. In a restricted range, we confirm an averaged version of a recent conjecture about the asymptotics of this variance. This result is closely related to moments of DirichletL-functions, and our proof relies on the asymptotic large sieve.


1992 ◽  
Vol 61 (3) ◽  
pp. 271-287 ◽  
Author(s):  
Etienne Fouvry ◽  
Henryk Iwaniec ◽  
Nicholas Katz

2018 ◽  
Vol 14 (08) ◽  
pp. 2225-2238
Author(s):  
Jorge Luis Cimadevilla Villacorta

In this paper, we prove some inequalities about the partial sums [Formula: see text] and [Formula: see text], where [Formula: see text] is the divisor function.


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