Nonvanishing of Koecher-Maass series attached to Siegel cusp forms

We prove a nonvanishing result for Koecher-Maass series attached to Siegel cusp forms of weight k and degree n in certain strips on the complex plane. When n = 2, we prove such a result for forms orthogonal to the space of the Saito-Kurokawa lifts `up to finitely many exceptions', in bounded regions. (C) 2015 Elsevier Inc. All rights reserved.

L-infinity norms of holomorphic modular forms in the case of compact quotient

We prove a sub-convex estimate for the sup-norm of L-2-normalized holomorphic modular forms of weight k on the upper half plane, with respect to the unit group of a quaternion division algebra over Q. More precisely we show that when the L-2 norm of an eigenfunction f is one, parallel to f parallel to(infinity) <<(epsilon) k(1/2-1/33+epsilon) for any epsilon > 0 and for all k sufficiently large.

The X Chromosome of Hemipteran Insects: Conservation, Dosage Compensation and Sex-Biased Expression

Insects of the order Hemiptera (true bugs) use a wide range of mechanisms of sex determination, including genetic sex determination, paternal genome elimination, and haplodiploidy. Genetic sex determination, the prevalent mode, is generally controlled by a pair of XY sex chromosomes or by an XX/XO system, but different configurations that include additional sex chromosomes are also present. Although this diversity of sex determining systems has been extensively studied at the cytogenetic level, only the X chromosome of the model pea aphid Acyrthosiphon pisum has been analyzed at the genomic level, and little is known about X chromosome biology in the rest of the order. In this study, we take advantage of published DNA- and RNA-seq data from three additional Hemiptera species to perform a comparative analysis of the gene content and expression of the X chromosome throughout this clade. We find that, despite showing evidence of dosage compensation, the X chromosomes of these species show female-biased expression, and a deficit of male-biased genes, in direct contrast to the pea aphid X. We further detect an excess of shared gene content between these very distant species, suggesting that despite the diversity of sex determining systems, the same chromosomal element is used as the X throughout a large portion of the order.

Cuspidality and the growth of Fourier coefficients of modular forms : A survey

In this paper, we present a survey of the recent results on the characterization of the cuspidality of classical modular forms on various groups by a suitable growth of their Fourier coefficients.

A NOTE ON SMALL GAPS BETWEEN NONZERO FOURIER COEFFICIENTS OF CUSP FORMS

It is shown that there are infinitely many primitive cusp forms f of weight 2 with the property that for all X large enough, every interval (X, X + cX(1/4)), where c > 0 depends only on the form, contains an integer n such that the n-th Fourier coefficient of f is nonzero.