18 citations · 46 across the 16 of their papers we have counts for
16 papers · 1 filter
On the hyperbolic prime number theorem
Alisa Sedunova
Friedlander and Iwaniec proved that the number of points of the orbit $\{γi \colon γ\in\SL_2(\Z)\}$ lying at a distance from the origin of the upper half-plane, with $p\l…
Relative class numbers and Euler-Kronecker constants of maximal real cyclotomic subfields
Neelam Kandhil, Alessandro Languasco, Pieter Moree +2
The Euler--Kronecker constant of a number field is the ratio of the constant and the residue of the Laurent series of the Dedekind zeta function at . We study the…
The Kummer ratio of the relative class number for prime cyclotomic fields
Neelam Kandhil, Alessandro Languasco, Pieter Moree +2
Kummer's conjecture predicts the asymptotic growth of the relative class number of prime cyclotomic fields. We substantially improve the known bounds of Kummer's ratio under three…
The multiplication table constant and sums of two squares
Andrew Granville, Cihan Sabuncu, Alisa Sedunova
We will show that the number of integers that can be written as the square of an integer plus the square of a prime equals minus a seco…
A higher order Levin-Feinleib theorem
Olivier Ramare, Alisa Sedunova, Ritika Sharma
When restricted to some non-negative multiplicative function, say f, bounded on primes and that vanishes on non square-free integers, our result provides us with an asymptotic for…
Intersections of binary quadratic forms in primes and the paucity phenomenon
Alisa Sedunova
The number of solutions to in integers is a well-known result, while if one restricts all the variables to primes Erdos showed that only the diagonal soluti…
Computation of the Kummer ratio of the class number for prime cyclotomic fields
Alessandro Languasco, Pieter Moree, Sumaia Saad Eddin +1
Let be a primitive root of unity with an arbitrary odd prime. The ratio of Kummer's first factor of the class number of the cyclotomic number field $\math…
A computational history of prime numbers and Riemann zeros
Pieter Moree, Izabela Petrykiewicz, Alisa Sedunova
We give an informal survey of the historical development of computations related to prime number distribution and zeros of the Riemann zeta function.
Jordan totient quotients
Pieter Moree, Sumaia Saad Eddin, Alisa Sedunova +1
The Jordan totient can be defined by . In this paper, we study the average behavior of fractions of two products and of…
Constrained ternary integers
Florian Luca, Pieter Moree, Robert Osburn +2
An integer is said to be ternary if it is composed of three distinct odd primes. In this paper, we asymptotically count the number of ternary integers with the const…
Bounds for the integral points on elliptic curves over function fields
Alisa Sedunova
In this paper we give an upper bound for the number of integral points on an elliptic curve E over F_q[T] in terms of its conductor N and q. We proceed by applying the lower bounds…
A logarithmic improvement in the Bombieri-Vinogradov theorem
Alisa Sedunova
In this paper we improve the best known to date result of Dress-Iwaniec-Tenenbaum, getting (log x)^2 instead of (log x)^(5/2). We use a weighted form of Vaughan's identity, allowin…
A variant of Bombieri-Vinogradov theorem with explicit constants
Alisa Sedunova
In this paper we improve the result of Akbary and Hambrook by a factor of log x by obtaining a better version of Vaughan's inequality and using the explicit variant of an inequalit…
On the Bombieri-Pila Method Over Function Fields
A. Sedunova
E. Bombieri and J. Pila introduced a method for bounding the number of integral lattice points that belong to a given arc under several assumptions. In this paper we generalize the…
On the asymptotic formulae for some multiplicative functions in short intervals
A. A. Sedunova
In this paper we prove the mean values of some multiplicative functions connected with the divisor function on the short interval of summation.
On the mean values of some multiplicative functions on the short interval
Alisa Sedunova
In this paper we study the mean values of some multiplicative functions connected with the divisor function on the short interval of summation. The asymptocic values for such mean…