S. Garcia

activity

20092026

most citedMathematical and physical aspects of complex symmetric operators

149 citations · 319 across the 56 of their papers we have counts for

collaborators

Showing 2017Show all

4 papers · 1 filter

math.NT2017

Primitive root biases for prime pairs I: existence and non-totality of biases

Stephan Ramon Garcia, Florian Luca, Timothy Schaaff

We study the difference between the number of primitive roots modulo $p$ and modulo $p + k$ for prime pairs $p, p + k$ . Assuming the Bateman-Horn conjecture, we prove the existence of s…

math.NT2017

On the difference in values of the Euler totient function near prime arguments

Stephan Ramon Garcia, Florian Luca

We prove unconditionally that for each $ℓ \geq 1$ , the difference $ϕ (p - ℓ) - ϕ (p + ℓ)$ is positive for $50%$ of odd primes $p$ and negative for $50%$ .

math.FA2017

Matrices similar to partial isometries

Stephan Ramon Garcia, David Sherman

We determine when a matrix is similar to a partial isometry, refining a result of Halmos--McLaughlin.

math.FA2017

Supercharacters and the discrete Fourier, cosine, and sine transforms

Stephan Ramon Garcia, Samuel Yih

Using supercharacter theory, we identify the matrices that are diagonalized by the discrete cosine and discrete sine transforms, respectively. Our method affords a combinatorial in…