On Short Exponential Sums Involving Fourier Coefficients of Holomorphic Cusp Forms

By an exponential sum of the Fourier coefficients of a holomorphic cusp form we mean the sum which is formed by first taking the Fourier series of the said form,then cutting the beginning and the tail away and considering the remaining sum on the real axis. For simplicity’s sake, typically the coefficients are normalized. However, this isn’t so important as the normalization can be done and removed simply by using partial summation. We improve the approximate functional equation for the exponential sums of the Fourier coefficients of the holomorphic cusp forms by giving an explicit upper bound for the error term appearing in the equation. The approximate functional equation is originally due to Jutila [9] and a crucial tool for transforming sums into shorter sums. This transformation changes the point of the real axis on which the sum is to be considered. We also improve known upper bounds for the size estimates of the exponential sums. For very short sums we do not obtain any better estimates than the very easy estimate obtained by multiplying the upper bound estimate for a Fourier coefficient (they are bounded by the divisor function as Deligne [2] showed) by the number of coefficients. This estimate is extremely rough as no possible cancellation is taken into account. However, with small sums, it is unclear whether there happens any remarkable amounts of cancellation.

Scherzando

Simananniemen käsikirjoituskokoelma.

Grand sonata Piano Forte and Violoncello Op 17

Sello, piano

Grand sonata Piano forte and Violoncello No 1 Op 5

Museokokoelma: 005.

Grand sonata Piano forte and Violoncello No 2 Op 5

Sello, piano

Grand sonata Piano forte and Violoncello No 1 Op102

Museokokoelma: 005.

Grand sonata Piano forte and Violoncello No 2 Op 102

Museokokoelma: 005.

Sonate für Pianoforte & Violoncello, Op121

Museokokoelma: 052.

Demographic Modelling of Human Population Growth

This work presents models and methods that have been used in producing forecasts of population growth. The work is intended to emphasize the reliability bounds of the model forecasts. Leslie model and various versions of logistic population models are presented. References to literature and several studies are given. A lot of relevant methodology has been developed in biological sciences. The Leslie modelling approach involves the use of current trends in mortality,fertility, migration and emigration. The model treats population divided in age groups and the model is given as a recursive system. Other group of models is based on straightforward extrapolation of census data. Trajectories of simple exponential growth function and logistic models are used to produce the forecast. The work presents the basics of Leslie type modelling and the logistic models, including multi- parameter logistic functions. The latter model is also analysed from model reliability point of view. Bayesian approach and MCMC method are used to create error bounds of the model predictions.

Quasiconformal mappings and inequalities involving special functions

This PhD thesis in Mathematics belongs to the field of Geometric Function Theory. The thesis consists of four original papers. The topic studied deals with quasiconformal mappings and their distortion theory in Euclidean n-dimensional spaces. This theory has its roots in the pioneering papers of F. W. Gehring and J. Väisälä published in the early 1960’s and it has been studied by many mathematicians thereafter. In the first paper we refine the known bounds for the so-called Mori constant and also estimate the distortion in the hyperbolic metric. The second paper deals with radial functions which are simple examples of quasiconformal mappings. These radial functions lead us to the study of the so-called p-angular distance which has been studied recently e.g. by L. Maligranda and S. Dragomir. In the third paper we study a class of functions of a real variable studied by P. Lindqvist in an influential paper. This leads one to study parametrized analogues of classical trigonometric and hyperbolic functions which for the parameter value p = 2 coincide with the classical functions. Gaussian hypergeometric functions have an important role in the study of these special functions. Several new inequalities and identities involving p-analogues of these functions are also given. In the fourth paper we study the generalized complete elliptic integrals, modular functions and some related functions. We find the upper and lower bounds of these functions, and those bounds are given in a simple form. This theory has a long history which goes back two centuries and includes names such as A. M. Legendre, C. Jacobi, C. F. Gauss. Modular functions also occur in the study of quasiconformal mappings. Conformal invariants, such as the modulus of a curve family, are often applied in quasiconformal mapping theory. The invariants can be sometimes expressed in terms of special conformal mappings. This fact explains why special functions often occur in this theory.

Thermal-Aware Networked Many-Core Systems

Advancements in IC processing technology has led to the innovation and growth happening in the consumer electronics sector and the evolution of the IT infrastructure supporting this exponential growth. One of the most difficult obstacles to this growth is the removal of large amount of heatgenerated by the processing and communicating nodes on the system. The scaling down of technology and the increase in power density is posing a direct and consequential effect on the rise in temperature. This has resulted in the increase in cooling budgets, and affects both the life-time reliability and performance of the system. Hence, reducing on-chip temperatures has become a major design concern for modern microprocessors. This dissertation addresses the thermal challenges at different levels for both 2D planer and 3D stacked systems. It proposes a self-timed thermal monitoring strategy based on the liberal use of on-chip thermal sensors. This makes use of noise variation tolerant and leakage current based thermal sensing for monitoring purposes. In order to study thermal management issues from early design stages, accurate thermal modeling and analysis at design time is essential. In this regard, spatial temperature profile of the global Cu nanowire for on-chip interconnects has been analyzed. It presents a 3D thermal model of a multicore system in order to investigate the effects of hotspots and the placement of silicon die layers, on the thermal performance of a modern ip-chip package. For a 3D stacked system, the primary design goal is to maximise the performance within the given power and thermal envelopes. Hence, a thermally efficient routing strategy for 3D NoC-Bus hybrid architectures has been proposed to mitigate on-chip temperatures by herding most of the switching activity to the die which is closer to heat sink. Finally, an exploration of various thermal-aware placement approaches for both the 2D and 3D stacked systems has been presented. Various thermal models have been developed and thermal control metrics have been extracted. An efficient thermal-aware application mapping algorithm for a 2D NoC has been presented. It has been shown that the proposed mapping algorithm reduces the effective area reeling under high temperatures when compared to the state of the art.

Ingest into the Digital Preservation Network: Standard Pipelines

Presentation at Open Repositories 2014, Helsinki, Finland, June 9-13, 2014