$PRIM prime

Latest papers

1. The large sieve inequality and additive decompositions of sums of squares math.NT · 14 Oct · 1 hit

   …on the large sieve, we prove a new sieve estimate for sets which are missing various residue classes modulo prime squares. For certain interesting residue class configurations, our bound is a significant improvement…

2. On the Structure of Radical Towers and their Parametrizations math.AG · 14 Oct · 1 hit

   …the tower variety depends only on the tower and that the incidence variety is always irreducible, so that no prime decomposition is needed. Moreover, we show how to replace a tower by an isomorphic one whose tower…

3. S-squareful values of binary quadratic forms math.NT · 14 Oct · 1 hit

   …and V\'arilly-Alvarado. In this paper, $S$-squareful values of this form are considered for $S$ the set of primes that divide $a$ and $b$. We prove an asymptotic formula for these numbers and show that the leading…

4. Quantitative lower bound for Pythagorean pairs in boxes of prime powers math.NT · 14 Oct · 2 hits

   For each positive integer $N$, let $p_i$ be the $i$-th prime for $i\in\{1,\ldots,N\}$, and set $$…

5. An upper bound for valuations of elliptic nets at primes of bad reduction math.NT · 14 Oct · 2 hits

   …2\nu(\Psi_{(v_1, v_2)}(\mathbf{P})))$, where $\nu$ is a normalised discrete valuation associated to primes where $E$ has bad reduction and $\Psi^2_{(v_1, v_2)}(\mathbf{P})$, $\Phi_{(v_1, v_2)}(\mathbf{P})$ are…

6. The finite basis problem and subvariety intervals for max-plus matrix semirings math.GR · 14 Oct · 1 hit

   …a chain and an antichain of that cardinality. The proof uses finite syntactic semirings associated with prime-cycle languages and an independent family of identities. We then construct finite commutative…

7. On the Hardy--Littlewood--Chowla conjecture math.NT · 14 Oct · 2 hits

   …at least to Hildebrand's work in 1989, asserts that the M\"obius function exhibits cancellation on shifted primes; that is, $$\sum_{p\le x}\mu(p+2)=o(\pi(x)),\quad \text{or equivalently}\quad \sum_{n\le…

8. Genus character $L$-functions of orders in quadratic function fields math.NT · 14 Oct · 1 hit

   …characteristic. We express each as a product of two quadratic $L$-functions and explicit local factors at primes dividing the conductor, with a possible shift of the variable in one of the two quadratic…