Hybrid subconvexity for class group LL-functions and uniform sup norm bounds of Eisenstein series

In this paper we prove a hybrid subconvexity bound for class group $L$-functions associated to a quadratic extension $K/\mathbb{Q}$ (real or imaginary). Our proof relies on relating the class group $L$-functions to Eisenstein series evaluated at Heegner points using formulas due to Hecke. The main technical contribution is the following uniform sup norm bound for Eisenstein series; $$E(z,1/2+it)\ll_\varepsilon y^{1/2} (|t|+1)^{1/3+\varepsilon},\quad y\gg 1,$$ extending work of Blomer and Titchmarsh. Finally we propose a uniform version of the sup norm conjecture for Eisenstein series.Comment: 21 pages, with an improved result ($y^{5/6}$ reduced to $y^{1/2}$ in the uniform sup norm bound) and furthermore the present version avoids the use of Duke's equidistribution of Heegner points making the paper more self-containe

Composting poultry manure by fly larvae (Musca domestica) eliminates Campylobacter jejuni from the manure

Introduction The common house fly, Musca domestica (Md) is an important carrier of zoonotic agents, and Campylobacter jejuni is one that may be transmitted between animals and humans by flies. Colonized animals shed the bacteria in feces where larval stages of Md flies develops. Aim of the present study To monitor fly larvae composting of poultry manure artificially contaminated with C. jejuni, and to investigate a possible transmission route of C. jejuni from the manure through the fly larvae to the adult fly. Conclusions The addition of fly larvae both accelerated the degradation of manure and C. jejuni. Pupae or newly hatched flies were not carriers of C. jejuni although larvae were grown in contaminated manure. Impact When composting poultry manure with Md fly larvae, it is possible both to reduce the amount of waste and to sanitize it from C. jejuni, thereby reducing the risk of contaminating the environment

Beskrivelse af en fluelarveinfektionsmodel

Beskrivelse af laboratorieinfektionsmodel til studie af fluelarver og patogener i gødning

Stuefluens larver kan inaktivere uønskede bakterier i gødning

Den almindelige stueflue (Musca domestica) er allesteds nærværende fra polare egne til troperne. Selvom fluens larvestadium foregår i rådnende organisk materiale eller gødning fra dyr og mennesker, tyder ny forskning på at larvens omsætning af gødningen er en vigtig og aktiv medspiller i elimineringen af uønskede bakterier som fx Campylobacter jejuni

Insekter - fra skadedyr til nyttedyr

Mens stuefluens larver vokser sig store, omsætter de hønsegødningen til pottemuld. De voksne larver udgør et proteinrigt foder, som hønerne er mere end villige til at spise

Equidistribution of qq-orbits of closed geodesics

We introduce a natural way of associating oriented closed geodesics on the modular curve to elements of $(\mathbb{Z}/q\mathbb{Z})^\times$ and prove that the corresponding packets associated to sufficiently large subgroups equidistribute in the unit tangent bundle as $q$ tends to infinity. This is a $q$-orbit analogue of Duke's Theorem for real quadratic field as extended to subgroups by Popa. We also show that the homology classes of the $q$-orbits of oriented closed geodesics concentrate around the Eisenstein line and present group theoretic applications thereof.Comment: 37 page

Residual equidistribution of modular symbols and cohomology classes for quotients of hyperbolic nn-space

We provide a new and simple automorphic method using Eisenstein series tostudy the equidistribution of modular symbols modulo primes, which we apply toprove an average version of a conjecture of Mazur and Rubin. More precisely, weprove that modular symbols corresponding to a Hecke basis of weight 2 cuspforms are asymptotically jointly equidistributed mod $p$ while we allowrestrictions on the location of the cusps. As an application, we obtain aresidual equidistribution result for Dedekind sums. Furthermore, we calculatethe variance of the distribution and show a surprising bias with connections toperturbation theory. Additionally, we prove the full conjecture in someparticular cases using a connection to Eisenstein congruences. Finally, ourmethods generalise to equidistribution results for cohomology classes of finitevolume quotients of $n$-dimensional hyperbolic space.<br