scholarly journals ON THE ERROR TERM IN THE PRIME GEODESIC THEOREM

2012 ◽  
Vol 49 (2) ◽  
pp. 367-372 ◽  
Author(s):  
Muharem Avdispahic ◽  
Dzenan Gusic
Author(s):  
OLGA BALKANOVA ◽  
DMITRY FROLENKOV ◽  
MORTEN S. RISAGER

Abstract The Zagier L-series encode data of real quadratic fields. We study the average size of these L-series, and prove asymptotic expansions and omega results for the expansion. We then show how the error term in the asymptotic expansion can be used to obtain error terms in the prime geodesic theorem.


2018 ◽  
Vol 70 (2) ◽  
pp. 649-674 ◽  
Author(s):  
Olga Balkanova ◽  
Dmitry Frolenkov

Abstract We develop a new method for studying sums of Kloosterman sums related to the spectral exponential sum. As a corollary, we obtain a new proof of the estimate of Soundararajan and Young for the error term in the prime geodesic theorem.


In 1949, A. Selberg discovered a real variable (an elementary) proof of the prime number theorem. A number of authors have adapted Selberg’s method to achieve quite a good corresponding error term. The Riemann hypothesis has never been proved or disproved however. Any generalization of the prime number theorem to the more general situations is known in literature as a prime geodesic theorem. In this paper we derive yet another proof of the prime geodesic theorem for compact symmetric spaces formed as quotients of the Lie group SL4 (R). While the first known proof in this setting applies contour integration over square boundaries, our proof relies on an application of modified circular boundaries. Recently, A. Deitmar and M. Pavey applied such prime geodesic theorem to derive an asymptotic formula for class numbers of orders in totally complex quartic fields with no real quadratic subfields.


Author(s):  
Olga Balkanova ◽  
Dmitry Frolenkov

We prove a new upper bound on the second moment of Maass form symmetric square L-functions defined over Gaussian integers. Combining this estimate with the recent result of Balog–Biro–Cherubini–Laaksonen, we improve the error term in the prime geodesic theorem for the Picard manifold.


The purpose of this paper is two-sided. First, we obtain the correct estimate of the error term in the classical prime geodesic theorem for compact symmetric space SL4. As it turns out, the corrected error term depends on the degree of a certain polynomial appearing in the functional equation of the attached zeta function. This is in line with the known result in the case of compact Riemann surface, or more generally, with the corresponding result in the case of compact locally symmetric spaces of real rank one. Second, we derive a weighted form of the theorem. In particular, we prove that the aforementioned error term can be significantly improved when the classical approach is replaced by its higher level analogue.


2002 ◽  
Vol 14 (6) ◽  
Author(s):  
Jay Jorgenson ◽  
Jürg Kramer

2020 ◽  
pp. 016327872098559
Author(s):  
Michael T. McKay ◽  
Frank C. Worrell ◽  
Jon C. Cole

The Adolescent and Adult Time Inventory–Time Attitudes Scale (AATI-TA) measures emotional engagement with the past, present, and future, and scores have been shown to relate meaningfully to health outcomes. For past, present, and future, five items are used to assess both positive and negative attitudes. Although evidence for the hypothesized six-factor solution has been widely reported, some studies have indicated problems with the Future Negative items. Given that a large and growing literature has emerged on the six-factor AATI-TA, and that AATI-TA scores have shown much better and more consistent fit than other temporal psychology measures, we sought to investigate the future negative factor in detail. Secondary analyses were performed on two datasets. The first was a University convenience sample ( N = 410) and the second was an adolescent sample ( N = 1,612). Confirmatory factor analyses revealed that the fit for the five Future Negative items was poor. Modification indices suggested that a correlated error term between Items 4 and 10 would result in good fit, and this was indeed the case. Models without Item 4 or Item 10 also yielded acceptable fit. Analyses using all four operationalizations of Future Negative (original scale, without Item 4 or Item 10, or with the correlated error between Items 4 and 10) to predict symptoms of anxiety and depression, and emotional self-efficacy revealed minor differences in the predictive validity coefficients. Potential ways forward, including a correlated error term or the dropping or replacement of Item 10, are discussed.


2021 ◽  
Vol 11 (4) ◽  
pp. 1873
Author(s):  
José Robinson Ortiz-Castrillón ◽  
Gabriel Eduardo Mejía-Ruiz ◽  
Nicolás Muñoz-Galeano ◽  
Jesús María López-Lezama ◽  
Juan Bernardo Cano-Quintero

This paper proposes a new sliding surface for controlling a Semi-Bridgeless Boost Converter (SBBC) which simultaneously performs Power Factor Correction (PFC) and DC bus regulation. The proposed sliding surface is composed of three terms: First, a normalized DC voltage error term controls the DC bus and rejects DC voltage disturbances. In this case, the normalization was performed for increasing system robustness during start-up and large disturbances. Second, an AC current error term implements a PFC scheme and guarantees fast current stabilization during disturbances. Third, an integral of the AC current error term increases stability of the overall system. In addition, an Adaptive Hysteresis Band (AHB) is implemented for keeping the switching frequency constant and reducing the distortion in zero crossings. Previous papers usually include the first and/or the second terms of the proposed sliding surface, and none consider the AHB. To be best of the author’s knowledge, the proposed Sliding Mode Control (SMC) is the first control strategy for SBBCs that does not require a cascade PI or a hybrid PI-Sliding Mode Control (PI-SMC) for simultaneously controlling AC voltage and DC current, which gives the best dynamic behavior removing DC overvoltages and responding fast to DC voltage changes or DC load current perturbations. Several simulations were carried out to compare the performance of the proposed surface with a cascade PI control, a hybrid PI-SMC and the proposed SMC. Furthermore, a stability analysis of the proposed surface in start-up and under large perturbations was performed. Experimental results for PI-SMC and SMC implemented in a SBBC prototype are also presented.


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