1,720,975 research outputs found
Half-integral weight Kloosterman sums and integer partitions
No full textSubmission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-05-01The student, Qihang Sun, accepted the attached license on 2024-04-22 at 20:45.The student, Qihang Sun, submitted this Dissertation for approval on 2024-04-22 at 20:47.This Dissertation was approved for publication on 2024-04-24 at 15:19.DSpace SAF Submission Ingestion Package generated from Vireo submission #20556 on 2024-09-16 at 00:44:22Kloosterman sums are special exponential sums which appear in many problems in number theory. Kloosterman first introduced these sums in \cite{Kloosterman1926firstdef} to investigate whether the quadratic form with fixed represents all sufficiently large natural numbers. Another application is to estimate the shifted sum of divisor functions. Let be the number of divisors of the positive integer and D(N,f)\defeq \sum_{n=1}^N \tau(n)\tau(n+h),\quad \text{for some fixed integer }h\geq 1. Heath-Brown \cite{HeathBrown1979ShiftedDivisor} applied the Weil bound \eqref{Weilbound standard Kl sum} of Kloosterman sums to prove that D(N,f)=\text{explicit main terms}+O(N^{\frac 56+\ep}),\quad \text{uniformly for }1\leq h\leq N^{\frac 56}. Using Kuznetsov's trace formula, Deshouillers and Iwaniec \cite{DeshouillersIwaniec1982ShiftDivisor} obtained a much better error bound O(N^{\frac 23+\ep}) for all . The integer partition function , which is the number of ways to write as a sum of positive integers, has been researched for remarkable properties by Euler, Hardy and Ramanujan \cite{HardyRamanujan1918Asymp}. Rademacher's exact formula \cite{Rademacher1937pn} states that can be written as a sum of exponential sums. The generating function of is , where is Dedekind's eta function with and \im z>0. Since is a weight modular form, using the definition of multiplier systems, we are able to rewrite the exponential sums in Rademacher's exact formula as generalized Kloosterman sums. The bounds on Kloosterman sums give the growth rate of errors for such approximations. There are very famous congruence properties of the partition function by Ramanujan: p(5n+4)\equiv 0\Mod 5,\quad p(7n+5)\equiv 0\Mod7, \quad p(11n+6)\equiv 0\Mod {11}. In 1944, Dyson \cite{Dyson} defined the rank of a partition of . If we let denote the number of partitions of with rank congruent to a\Mod b, then Dyson conjectured that and for all . By the work of Bringmann and Ono \cite{BrmOno2006ivt,BrmOno2010}, the generating functions for the ranks of partitions have similar properties as . The work of Bringmann and Ono in the theory of harmonic Maass forms discovers beautiful properties about the rank of partitions. For example, in \cite{BrmOno2006ivt} they proved the exact formula for the modulo case, which perfected the asymptotics by Ramanujan, Dragonette \cite{Dragonette1952} and Andrews \cite{Andrews1966}. If we have better estimates for the sums of half-integral weight Kloosterman sums, we are able to obtain better tail bounds for the Rademacher-type exact formulas, which control the efficiency of their convergence. The recent work by Ahlgren and Andersen \cite{AAimrn}, Ahlgren and Dunn \cite{ahlgrendunn}, and Andersen and Wu \cite{AndersenWu2022bound36_publishedver} provide improved error bounds based on their improvement on the estimates for Kloosterman sums. The author \cite{QihangFirstAsympt,QihangSecondAsympt} generalized their work to the Kloosterman sums with a wider class of multiplier systems, which are half-integral weight and include the commonly used theta- and eta-multipliers twisted by quadratic characters. The resulting estimates give a uniform version of the general result by Goldfeld and Sarnak \cite{gs} for sums of such Kloosterman sums with a power-saving bound in the parameters and . Following the method in \cite{BrmOno2006ivt}, the author provided a detailed proof of the exact formula for the rank modulo 3 case in \cite{QihangFirstAsympt}. Then what about the exact formulae in the rank modulo 5 and 7 cases, where Ramanujan's congruences appear? Bringmann \cite{BringmannTAMS} proved the general asymptotics for all odd moduli, while the Kloosterman type sums are hard to interpret as Kloosterman sums. Thanks to the theory of vector-valued Maass forms from \cite{BrmOno2010} and the explicit transformation laws by Garvan \cite{GarvanTransformationDyson2017}, the author finds the interpretation as vector-valued Kloosterman sums. Combining with some generalization of \cite{gs}, the author finally provides the proof for the exact formula of rank modulo primes . The author also has a striking observation between the interesting cases , where the Kloosterman sums become identically zero (or become equal for those defined on different cusp pairs). After a long study of the cases depending on congruence properties of the Dedekind sums, the author proves this cancellation property and provides a new proof for the Dyson's conjecture and which implies Ramanujan's congruences
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
Topics in analytic number theory
Full text linkThis thesis, consisting of two chapters, proves several new theorems concerning L-functions and the distribution of primes.
In the first chapter, we establish the first explicit form of the Vinogradov–Korobov zero-free region for Dirichlet L-functions.
In the second chapter, we generalize recent work on large gaps between primes to imaginary quadratic fields. Suppose K is an imaginary quadratic field, and let N_K denote the field norm on O_K. For x₀ in O_K and r > 0, let (x₀, r) = { x in O_K : |N_K(x − x₀)| 0 : there exists x₀ in O_K such that |N_K(x₀)| ≤ X and B(x₀, r) contains no primes }. We show that G_K(X) is at least c_K (log X) (log₂ X · log₄ X) / log₃ X for some constant c_K > 0 depending only on K.Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2026-02-19 without embargo termsThe student, Tanmay Khale, accepted the attached license on 2025-12-03 at 10:19.The student, Tanmay Khale, submitted this Dissertation for approval on 2025-12-03 at 12:54.This Dissertation was approved for publication on 2025-12-05 at 10:40.DSpace SAF Submission Ingestion Package generated from Vireo submission #23040 on 2026-02-19 at 18:26:3
Author-wise bibliometric analysis based on entropy.
No full textAuthor-wise bibliometric analysis based on entropy.</p
- …
