Olivier Ramaré

most citedCounting ideals in ray classes

3 citations · 3 across the 5 of their papers we have counts for

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5 papers

math.NT2023

Explicit count of integral ideals of an imaginary quadratic field

Olivier Ramaré

We provide explicit bounds for the number of integral ideals of norms at most $X$ is $Q [d]$ when $d < 0$ is a fundamendal discriminant with an error term of size $O(…

math.NT2023

A Moebius sum

Olivier Ramaré

We provide numerical bounds for $Σ (X) = \sum_{d_{1}, d_{2} \leq X} \frac{μ ( d _{1} ) μ ( d _{2} )}{[ d _{1} , d _{2} ]}$ . We show in particular that $0 \leq Σ (X) \leq 17/25$ for every $X \geq 2$ .

math.NT2022

A modular analogue of a problem of Vinogradov

Ratnadeep Acharya, Sary Drappeau, Satadal Ganguly +1

Given a primitive, non-CM, holomorphic cusp form $f$ with normalized Fourier coefficients $a (n)$ and given an interval $I \subset [- 2, 2]$ , we study the least prime $p$ such that $a…

math.NT2022

Product of three primes in large arithmetic progressions

Ramachandran Balasubramanian, Olivier Ramaré, Priyamvad Srivastav

For any $ε > 0$ , there exists $q_{0} (ε)$ such for any $q \geq q_{0} (ε)$ and any invertible residue class $a$ modulo $q$ , there exists a natural number that is congruent to $a$ modulo $q$ a…

math.NT2022★ 3 cited

Counting ideals in ray classes

Sanoli Gun, Olivier Ramaré, Jyothsnaa Sivaraman

Let $K$ be a number field and $q$ an integral ideal in $O_{K}$ . A result of Tatuzawa from 1973, computes the asymptotic (with an error term)…