Related papers: An unexpected trace relation of CM points

Odd-frequency Cooper pairs are gathering attention for the convenience of investigating the edge state of topological superconductors including Majorana fermions. Although a spinless p-wave superconductor has only one Majorana fermion in a…

In this work, we theoretically study transverse magnetic focusing in a two-dimensional electron gas with strong Rashba spin-orbit interaction when proximitized along its edge with a superconducting contact. The presence of superconducting…

Let $K$ be an algebraically closed field of characteristic different from $2$, $g$ a positive integer, $f(x)\in K[x]$ a degree $2g+1$ monic polynomial without repeated roots, $C_f: y^2=f(x)$ the corresponding genus g hyperelliptic curve…

For CM elliptic curve over rational field with analytic rank one, for any potential good ordinary prime p, not dividing the number of roots of unity in the complex multiplication field, we show the p-part of its Shafarevich-Tate group has…

In this paper we study quadratic points on the non-split Cartan modular curves $X_{ns}(p)$, for $p = 7, 11,$ and $13$. Recently, Siksek proved that all quadratic points on $X_{ns}(7)$ arise as pullbacks of rational points on $X_{ns}^+(7)$.…

We prove, assuming the Generalized Riemann Hypothesis for imaginary quadratic fields, that irreducible curves in the product of two modular curves that contain infinitely many complex multiplication points are either a Hecke correspondence…

The nature of unconventional superconductivity is intimately linked to the microscopic nature of the pairing interactions. In this work, motivated by cubic heavy fermion compounds with embedded multipolar moments, we theoretically…

We analyze superconductivity in a multi-orbital fermionic system near the onset of a nematic order, using doped FeSe as an example. We associate the nematic order with spontaneous polarization between $d_{xz}$ and $d_{yz}$ orbitals. We…

Recent experiments on Cooper pair splitters using superconductor-quantum dot hybrids have embarked on creating entanglement in the solid-state, by engineering the sub-gap processes in the superconducting region. Using the thermoelectric…

A central puzzle in strongly correlated electronic phases is strange metallic transport, marked by $T$-linear resistivity and $B$-linear magnetoresistance, in sharp contrast with quadratic scalings observed in conventional metals. Here, we…

Let $K$ be a field of characteristic different from $2$, $\bar{K}$ its algebraic closure. Let $n \ge 3$ be an odd integer. Let $f(x)$ and $h(x)$ be degree $n$ polynomials with coefficients in $K$ and without repeated roots. Let us consider…

In this article, we classify the characters associated to algebraic points on Shimura curves of $\Gamma_0(p)$-type, and over a quadratic field we show that there are at most elliptic points on such a Shimura curve for every sufficiently…

Let $E$ be an elliptic curve defined over a number field $K$. We say that a prime number $p$ is exceptional for $(E,K)$ if $E$ admits a $p$-isogeny defined over $K$. The so-called exceptional set of all such prime numbers is finite if and…

Most studies of non-trivial topological systems are carried out in non-interacting models that admit an exact solution. This raises the question, to which extent the consideration of electronic correlations and disorder, present in real…

The results obtained in this paper grew from an attempt to generalize the main theorem of [1]. There it was shown that any circuit injection (a 1-1 onto edge map f such that if C is a circuit then f(C) is a circuit) from a 3-connected, not…

For E/k an elliptic curve with CM by O, we determine a formula for (a generalization of) the arithmetic local constant of [4] at almost all primes of good reduction. We apply this formula to the CM curves defined over Q and are able to…

The quest for high-temperature superconductivity at ambient pressure is a central issue in physics. In this regard, the relationship between unconventional superconductivity and the quantum critical point (QCP) associated with the…

We produce explicit elliptic curves over \Bbb F_p(t) whose Mordell-Weil groups have arbitrarily large rank. Our method is to prove the conjecture of Birch and Swinnerton-Dyer for these curves (or rather the Tate conjecture for related…

Let $C$ be a hyperelliptic curve $y^2 = f(x)$ over a discretely valued field $K$. The $p$-adic distances between the roots of $f(x)$ can be described by a completely combinatorial object known as the cluster picture. We show that the…

Signatures of unconventional superconductivity have been recently observed in certain transition metal dichalcogenides (TMDs), including 4H$_b$-TaS$_2$ and monolayer 2H-NbSe$_2$. While the pairing channel remains unknown, it has been argued…