Yuta Suzuki

Yuta Suzuki
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Yuta Suzuki
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Mathematics - Number Theory (4)
 
Physics - Strongly Correlated Electrons (1)
 
Physics - Superconductivity (1)
 
Mathematics - Differential Geometry (1)
 
Mathematics - Combinatorics (1)
 
Physics - Optics (1)

Publications Authored By Yuta Suzuki

Assuming a conjecture on distinct zeros of Dirichlet L-functions we get asymptotic results on the average number of representations of an integer as the sum of two primes in arithmetic progression. On the other hand the existence of good error terms gives information on the the location of zero free regions of L-functions and possible Siegel zeros. Similar results are obtained for an integer in a congruence class expressed as the sum of two primes. Read More

For a given pair of two graphs $(F,H)$, let $R(F,H)$ be the smallest positive integer $r$ such that for any graph $G$ of order $r$, either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. Baskoro, Broersma and Surahmat (2005) conjectured that \[ R(F_\ell,K_n)=2\ell(n-1)+1 \] for $\ell\ge n\ge3$, where $F_\ell$ is the join of $K_1$ and $\ell K_2$. In this paper, we prove that this conjecture is true for the case $n=6$. Read More

In this paper, we consider pairs of a prime and a prime power with a fixed difference. We prove an average result on the distribution of such pairs. This is a partial improvement of the result of Bauer (1998). Read More

Hardy and Littlewood conjectured that every sufficiently large integer is either a square or the sum of a prime and a square. Let $E(x)$ be the number of positive integers up to $x\ge4$ which does not satisfy this condition. We prove $E(x)\ll x^{1/2}(\log x)^A(\log\log x)^4$with $A=3/2$ under the Generalized Riemann Hypothesis. Read More

In this note, assuming a variant of the Generalized Riemann Hypothesis, which does not exclude the existence of real zeros, we prove an asymptotic formula for the mean value of the representation function for the sum of two primes in arithmetic progressions. This is an improvement of the result of F. R\"uppel in 2009, and the generalization of the result of A. Read More

Odaka and Wang proved the intersection formula for the Donaldson-Futaki invariant. In this paper, we generalize this result for the higher Futaki invariants which are obstructions to asymptotic Chow semistability. Read More

Focusing light into opaque random or scattering media such as biological tissue is a much sought-after goal for biomedical applications such as photodynamic therapy, optical manipulation, and photostimulation. However, focusing with conventional lenses is restricted to one transport mean free path in scattering media, limiting both optical penetration depth and resolution. Focusing deeper is possible by using optical phase conjugation or wavefront shaping to compensate for the scattering. Read More

Over the past 20 years, fullerides have been studied as the source of high-transition-temperature (Tc) superconductivity except for copper oxides. The recent finding of the Mott insulating state right beside superconductivity in Cs3C60 has suggested that magnetism helps raise Tc even in fullerides as in heavy-fermion compounds, high-Tc copper oxides, two-dimensional organic conductors, and iron pnictides. Namely, one tends to think that the link between Mott insulator and superconductivity takes place in fullerides, which can give rise to the mechanism beyond the Bardeen-Cooper-Schrieffer framework. Read More