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1. Multiplicity and rapidity dependence of $$\textrm{K}^{*}(\mathrm {{\textbf {892}}})^{0}$$ and $$\mathrm {\phi ({\textbf {1020}})}$$ production in p–Pb collisions at $$\sqrt{s_{\textrm{NN}}} =$$ 5.02 TeV

   https://doi.org/10.1140/epjc/s10052-023-11449-3  

   Acharya, S. ; Adamová, D. ; Adler, A. ; Aglieri Rinella, G. ; Agnello, M. ; Agrawal, N. ; Ahammed, Z. ; Ahmad, S. ; Ahn, S. U. ; Ahuja, I. ; et al ( June 2023 , The European Physical Journal C)

   Abstract The transverse-momentum $$(p_{\textrm{T}})$$ ( p T ) spectra of K $$^{*}(892)^{0}~$$ ∗ ( 892 ) 0 and $$\mathrm {\phi (1020)}~$$ ϕ ( 1020 ) measured with the ALICE detector up to $$p_{\textrm{T}} $$ p T  = 16 GeV/ c in the rapidity range $$-1.2< y < 0.3,$$ - 1.2 < y < 0.3 , in p–Pb collisions at the center-of-mass energy per nucleon–nucleon collision $$\sqrt{s_{\textrm{NN}}} = 5.02$$ s NN = 5.02  TeV are presented as a function of charged particle multiplicity and rapidity. The measured $$p_{\textrm{T}} $$ p T distributions show a dependence on both multiplicity and rapidity at low $$p_{\textrm{T}} $$ p T whereas no significant dependence is observed at high $$p_{\textrm{T}} $$ p T . A rapidity dependence is observed in the $$p_{\textrm{T}} $$ p T -integrated yield (d N /d y ), whereas the mean transverse momentum $$\left( \langle p_{\textrm{T}} \rangle \right) $$ ⟨ p T ⟩ shows a flat behavior as a function of rapidity. The rapidity asymmetry ( $$Y_{\textrm{asym}}$$ Y asym ) at low $$p_{\textrm{T}} $$ p T (< 5 GeV/ c ) is more significant for higher multiplicity classes. At high $$p_{\textrm{T}} $$ p T , no significant rapidity asymmetry is observed in any of the multiplicity classes. Both K $$^{*}(892)^{0}~$$ ∗ ( 892 ) 0 and $$\mathrm {\phi (1020)}~$$ ϕ ( 1020 ) show similar $$Y_{\textrm{asym}}$$ Y asym . The nuclear modification factor $$(Q_{\textrm{CP}})$$ ( Q CP ) as a function of $$p_{\textrm{T}} $$ p T shows a Cronin-like enhancement at intermediate $$p_{\textrm{T}} $$ p T , which is more prominent at higher rapidities (Pb-going direction) and in higher multiplicity classes. At high $$p_{\textrm{T}}$$ p T (> 5 GeV/ $$c$$ c ), the $$Q_{\textrm{CP}}$$ Q CP values are greater than unity and no significant rapidity dependence is observed. 

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2. On the nonvanishing of generalised Kato classes for elliptic curves of rank 2

   https://doi.org/10.1017/fms.2021.85  

   Castella, Francesc ; Hsieh, Ming-Lun ( January 2022 , Forum of Mathematics, Sigma)

   Abstract Let $E/\mathbf {Q}$ be an elliptic curve and $p>3$ be a good ordinary prime for E and assume that $L(E,1)=0$ with root number $+1$ (so $\text {ord}_{s=1}L(E,s)\geqslant 2$ ). A construction of Darmon–Rotger attaches to E and an auxiliary weight 1 cuspidal eigenform g such that $L(E,\text {ad}^{0}(g),1)\neq 0$ , a Selmer class $\kappa _{p}\in \text {Sel}(\mathbf {Q},V_{p}E)$ , and they conjectured the equivalence $$ \begin{align*} \kappa_{p}\neq 0\quad\Longleftrightarrow\quad{\textrm{dim}}_{{\mathbf{Q}}_{p}}\textrm{Sel}(\mathbf{Q},V_{p}E)=2. \end{align*} $$ In this article, we prove the first cases on Darmon–Rotger’s conjecture when the auxiliary eigenform g has complex multiplication. In particular, this provides a new construction of nontrivial Selmer classes for elliptic curves of rank 2. 

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3. Negative Moments of L –Functions With Small Shifts Over Function Fields

   https://doi.org/10.1093/imrn/rnad118  

   Florea, Alexandra ( June 2023 , International Mathematics Research Notices)

   We consider negative moments of quadratic Dirichlet $L$–functions over function fields. Summing over monic square-free polynomials of degree $2g+1$ in $\mathbb{F}_{q}[x]$, we obtain an asymptotic formula for the $k^{\textrm{th}}$ shifted negative moment of $L(1/2+\beta ,\chi _{D})$, in certain ranges of $\beta $ (e.g., when roughly $\beta \gg \log g/g $ and $k<1$). We also obtain non-trivial upper bounds for the $k^{\textrm{th}}$ shifted negative moment when $\log (1/\beta ) \ll \log g$. Previously, almost sharp upper bounds were obtained in [ 3] in the range $\beta \gg g^{-\frac{1}{2k}+\epsilon }$.

    

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4. Character bounds for regular semisimple elements and asymptotic results on Thompson’s conjecture

   https://doi.org/10.1007/s00209-022-03193-3  

   Larsen, Michael ; Taylor, Jay ; Tiep, Pham Huu ( February 2023 , Mathematische Zeitschrift)

   Abstract For every integer k there exists a bound $$B=B(k)$$ B = B ( k ) such that if the characteristic polynomial of $$g\in \textrm{SL}_n(q)$$ g ∈ SL n ( q ) is the product of $$\le k$$ ≤ k pairwise distinct monic irreducible polynomials over $$\mathbb {F}_q$$ F q , then every element x of $$\textrm{SL}_n(q)$$ SL n ( q ) of support at least B is the product of two conjugates of g . We prove this and analogous results for the other classical groups over finite fields; in the orthogonal and symplectic cases, the result is slightly weaker. With finitely many exceptions ( p ,  q ), in the special case that $$n=p$$ n = p is prime, if g has order $$\frac{q^p-1}{q-1}$$ q p - 1 q - 1 , then every non-scalar element $$x \in \textrm{SL}_p(q)$$ x ∈ SL p ( q ) is the product of two conjugates of g . The proofs use the Frobenius formula together with upper bounds for values of unipotent and quadratic unipotent characters in finite classical groups. 

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5. Jet-like correlations with respect to $$\textrm{K}^{0}_\mathrm{{S}}$$ and $$\Lambda $$ ($$\overline{\Lambda }$$) in pp and central Pb–Pb collisions at $$\mathbf {\sqrt{s_\textrm{NN}}} = 5.02$$ TeV

   https://doi.org/10.1140/epjc/s10052-023-11614-8  

   Acharya, S. ; Adamová, D. ; Adler, A. ; Aglieri Rinella, G. ; Agnello, M. ; Agrawal, N. ; Ahammed, Z. ; Ahmad, S. ; Ahn, S. U. ; Ahuja, I. ; et al ( June 2023 , The European Physical Journal C)

   Abstract Two-particle correlations with $$\textrm{K}^{0}_\mathrm{{S}}$$ K S 0 , $$\Lambda $$ Λ / $$\overline{\Lambda }$$ Λ ¯ , and charged hadrons as trigger particles in the transverse momentum range $$8{<}p_{{\textrm{T}},{\textrm{trig}}}{<}16$$ 8 < p T , trig < 16  GeV/ $$c$$ c , and associated charged particles within $$1{<}p_{{\textrm{T}},{\textrm{assoc}}}{<}8$$ 1 < p T , assoc < 8  GeV/ $$c$$ c , are studied at midrapidity in pp and central Pb–Pb collisions at a centre-of-mass energy per nucleon–nucleon collision $$\sqrt{s_{\textrm{NN}}}~=~5.02$$ s NN = 5.02  TeV with the ALICE detector at the LHC. After subtracting the contributions of the flow background, the per-trigger yields are extracted on both the near and away sides, and the ratio in Pb–Pb collisions with respect to pp collisions ( $$I_{\textrm{AA}}$$ I AA ) is computed. The per-trigger yield in Pb–Pb collisions on the away side is strongly suppressed to the level of $$I_{\textrm{AA}}$$ I AA $$\approx 0.6$$ ≈ 0.6 for $$p_{{\textrm{T}},{\textrm{assoc}}}>3$$ p T , assoc > 3  GeV/ $$c$$ c as expected from strong in-medium energy loss, while an enhancement develops at low $$p_{{\textrm{T}},{\textrm{assoc}}}$$ p T , assoc on both the near and away sides, reaching $$I_{\textrm{AA}}$$ I AA $$\approx 1.8$$ ≈ 1.8 and 2.7 respectively. These findings are in good agreement with previous ALICE measurements from two-particle correlations triggered by neutral pions ( $$\pi ^{0}$$ π 0 –h) and charged hadrons (h–h) in Pb–Pb collisions at $$\sqrt{s_{\textrm{NN}}}~=~2.76$$ s NN = 2.76  TeV. Moreover, the correlations with $$\textrm{K}^{0}_\mathrm{{S}}$$ K S 0 mesons and $$\Lambda $$ Λ / $$\overline{\Lambda }$$ Λ ¯ baryons as trigger particles are compared to those of inclusive charged hadrons. The results are compared with the predictions of Monte Carlo models. 

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