Zobrazeno 1 - 10
of 600
pro vyhledávání: '"Moree, P."'
The Euler-Kronecker constants related to congruences of Fourier coefficients of modular forms that have been computed so far, involve logarithmic derivatives of Dirichlet $L$-series as most complicated functions (to the best of our knowledge). Howeve
Externí odkaz:
http://arxiv.org/abs/2412.01803
Assuming the Generalized Riemann Hypothesis and a pair correlation conjecture for the zeros of Dirichlet $L$-functions, we establish the truth of a conjecture of Montgomery (in its corrected form stated by Friedlander and Granville) on the magnitude
Externí odkaz:
http://arxiv.org/abs/2411.19762
Autor:
Berndt, Bruce C., Moree, Pieter
Ramanujan, in his famous first letter to Hardy, claimed a very precise estimate for the number of integers that can be written as a sum of two squares. Far less well-known is that he also made further claims of a similar nature for the non-divisibili
Externí odkaz:
http://arxiv.org/abs/2409.03428
The Euler--Kronecker constant of a number field $K$ is the ratio of the constant and the residue of the Laurent series of the Dedekind zeta function $\zeta_K(s)$ at $s=1$. We study the distribution of the Euler--Kronecker constant $\gamma_q^+$ of the
Externí odkaz:
http://arxiv.org/abs/2407.09113
Autor:
Languasco, Alessandro, Moree, Pieter
Publikováno v:
Math. Comp. 2025
Many Dirichlet series of number theoretic interest can be written as a product of generating series $\zeta_{\,d,a}(s)=\prod\limits_{p\equiv a\pmod{d}}(1-p^{-s})^{-1}$, with $p$ ranging over all the primes in the primitive residue class modulo $a\pmod
Externí odkaz:
http://arxiv.org/abs/2406.16547
Autor:
Morée, Jean-Baptiste, Arita, Ryotaro
We explore the possibility to control the superconducting (SC) transition temperature at optimal hole doping $T_{c}^{\rm opt}$ in cuprates by tuning the chemical formula (CF). $T_{c}^{\rm opt}$ can be theoretically predicted from the parameters of th
Externí odkaz:
http://arxiv.org/abs/2403.07525
The Brauer-Siegel theorem concerns the size of the product of the class number and the regulator of a number field $K$. We derive bounds for this product in case $K$ is a prime cyclotomic field, distinguishing between whether there is a Siegel zero o
Externí odkaz:
http://arxiv.org/abs/2402.13830
Kummer's conjecture predicts the asymptotic growth of the relative class number of prime cyclotomic fields. We substantially improve the known bounds of Kummer's ratio under three scenarios: no Siegel zero, presence of Siegel zero and assuming the Ri
Externí odkaz:
http://arxiv.org/abs/2402.13829
The superconducting (SC) cuprate HgBa$_2$Ca$_2$Cu$_3$O$_8$ (Hg1223) has the highest $T_{c}^{\rm opt}\simeq 138$ K (the experimental SC transition temperature at optimal hole doping) among cuprates at ambient pressure $P_{\rm amb}$. $T_{c}^{\rm opt}$
Externí odkaz:
http://arxiv.org/abs/2312.16402
The family of Shallit sequences consists of the Lucas sequences satisfying the recurrence $U_{n+2}(k)=(4k+2)U_{n+1}(k) -U_n(k),$ with initial values $U_0(k)=0$ and $U_1(k)=1$ and with $k\ge 1$ arbitrary. For every fixed $k$ the integers $\{U_n(k)\}_{
Externí odkaz:
http://arxiv.org/abs/2309.12843