A Generous Bound for Divisor Sums: 10949

2004 ◽  
Vol 111 (3) ◽  
pp. 264
Author(s):  
Jeffrey Lagarias ◽  
Walther Janous
Keyword(s):  
Divisor Sums

Weighted divisor sums and Bessel function series, IV

2012 ◽  
Vol 29 (1-3) ◽  
pp. 79-102 ◽  
Author(s):  
Bruce C. Berndt ◽  
Sun Kim ◽  
Alexandru Zaharescu
Keyword(s):  
Bessel Function ◽  
Function Series ◽  
Divisor Sums

Divisor Sums of Generalised Exponential Polynomials

1996 ◽  
Vol 39 (1) ◽  
pp. 35-46 ◽  
Author(s):  
G. R. Everest ◽  
I. E. Shparlinski
Keyword(s):  
Prime Ideal ◽  
Algebraic Integer ◽  
Linear Recurrence ◽  
Exponential Polynomial ◽  
Exponential Polynomials ◽  
Recurrence Sequence ◽  
Special Cases ◽  
Divisor Sums ◽  
Recurrence Sequences

AbstractA study is made of sums of reciprocal norms of integral and prime ideal divisors of algebraic integer values of a generalised exponential polynomial. This includes the important special cases of linear recurrence sequences and general sums of S-units. In the case of an integral binary recurrence sequence, similar (but stronger) results were obtained by P. Erdős, P. Kiss and C. Pomerance.

scholarly journals Moments of zeta and correlations of divisor‐sums: V

2018 ◽  
Vol 118 (4) ◽  
pp. 729-752 ◽  
Author(s):  
Brian Conrey ◽  
Jonathan P. Keating
Keyword(s):  
Divisor Sums

scholarly journals The variance of divisor sums in arithmetic progressions

2018 ◽  
Vol 30 (2) ◽  
pp. 269-293
Author(s):  
Brad Rodgers ◽  
Kannan Soundararajan
Keyword(s):  
Arithmetic Progressions ◽  
Large Sieve ◽  
Restricted Range ◽  
Divisor Function ◽  
Residue Classes ◽  
Divisor Sums

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.

Logarithmic means and double series of Bessel functions

2015 ◽  
Vol 11 (05) ◽  
pp. 1535-1556 ◽  
Author(s):  
Bruce C. Berndt ◽  
Sun Kim
Keyword(s):  
Bessel Functions ◽  
Double Series ◽  
Logarithmic Mean ◽  
Riesz Mean ◽  
Lost Notebook ◽  
Logarithmic Means ◽  
Divisor Problems ◽  
Divisor Sums

In his lost notebook, Ramanujan recorded two identities involving double series of Bessel functions that are closely connected with the classical, unsolved circle and divisor problems. In a series of papers with Zaharescu, the authors proved these identities under various interpretations, as well as Riesz mean analogues. In this paper, logarithmic mean analogues, also involving double series of Bessel functions, are established. Weighted divisor sums involving characters play a central role.

scholarly journals Moments of zeta and correlations of divisor-sums: IV

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Brian Conrey ◽  
Jonathan P. Keating
Keyword(s):  
Divisor Sums
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