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math.NT2018
New upper bounds for the number of divisors function
Jean-Marie De Koninck, Patrick Letendre
Let stand for the number of divisors of the positive integer . We obtain upper bounds for in terms of and the number of distinct prime factors of .
math.NT2018
The larger sieve and polynomial congruences
Patrick Letendre
We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomi…