Sums of Kloosterman Sums.
Sums of k-th powers in the ring of polynomials with integer coefficients
Sums of L-functions over rational function fields
Sums of like powers and some dense sets.
Sums of mixed powers in fields and orderings of prescribed level.
Sums of multiplicative function in special arithmetic progressions
We find, via the Selberg-Delange method, an asymptotic formula for the mean of arithmetic functions on certain APs. It generalizes a result due to Cui and Wu (2014).
Sums of nine squares
Sums of nonnegative multiplicative functions over integers without large prime factors II
Sums of nonnegative multiplicative functions over integers without large prime factors I
Sums of one prime and two prime squares
Sums of Periodicals of Certain Additive Functions.
Sums of positive density subsets of the primes
We show that if A and B are subsets of the primes with positive relative lower densities α and β, then the lower density of A+B in the natural numbers is at least , which is asymptotically best possible. This improves results of Ramaré and Ruzsa and of Chipeniuk and Hamel. As in the latter work, the problem is reduced to a similar problem for subsets of using techniques of Green and Green-Tao. Concerning this new problem we show that, for any square-free m and any of densities α and β, the...
Sums of Powered Characteristic Roots Count Distance-Independent Circular Sets
Significant values of a combinatorial count need not fit the recurrence for the count. Consequently, initial values of the count can much outnumber those for the recurrence. So is the case of the count, Gl(n), of distance-l independent sets on the cycle Cn, studied by Comtet for l ≥ 0 and n ≥ 1 [sic]. We prove that values of Gl(n) are nth power sums of the characteristic roots of the corresponding recurrence unless 2 ≤ n ≤ l. Lucas numbers L(n) are thus generalized since L(n) is the count in question...
Sums of powers: an arithmetic refinement to the probabilistic model of Erdős and Rényi
Erdős and Rényi proposed in 1960 a probabilistic model for sums of s integral sth powers. Their model leads almost surely to a positive density for sums of s pseudo sth powers, which does not reflect the case of sums of two squares. We refine their model by adding arithmetical considerations and show that our model is in accordance with a zero density for sums of two pseudo-squares and a positive density for sums of s pseudo sth powers when s ≥ 3. Moreover, our approach supports a conjecture of...
Sums of powers in rings and the real holomorphy ring.
Sums of Powers of Cusp Form Coefficients.
Sums of Powers of Cusp Form Coefficients. II.
Sums of powers of generators of a finite field
Sums of Prime Powers.
Sums of Products of Certain Arthmetical Functions