scholarly journals Non-vanishing of Maass form $L$-functions at the central point

2020 ◽  
pp. 1
Author(s):  
Olga Balkanova ◽  
Bingrong Huang ◽  
Anders Södergren
Keyword(s):  
Central Point ◽  
Maass Form

scholarly journals Simultaneous non-vanishing of GL(3) × GL(2) and GL(2) L-functions

2011 ◽  
Vol 152 (3) ◽  
pp. 535-553 ◽  
Author(s):  
RIZWANUR KHAN
Keyword(s):  
Central Point ◽  
Maass Form ◽  
Average Value ◽  
Fixed Weight ◽  
The Family

AbstractFix g a Hecke–Maass form for SL3(). In the family of holomorphic newforms f of fixed weight and large prime level q, we find the average value of the product $L(\half,g\times f)L(\half,f)$. From this we derive a result on the simultaneous non-vanishing of these L-functions at the central point.

Concept of Nabhi – A Review Study

2017 ◽  
Vol 2 (4) ◽  
Author(s):  
Kishor G. Satani ◽  
Hemang U. Raghavani ◽  
Kunjal H. Bhatt
Keyword(s):  
Contemporary Literature ◽  
Physiological Process ◽  
Central Point ◽  
Undigested Food ◽  
Review Study

The central point of body in between Amashaya (location of undigested food) and Pakvashaya (location of digested food) is termed as Nabhi. In classical texts of Ayurveda; scattered references regarding Nabhi are available like Nabhi is mentioned as a vital spot (Marma) of body. Nabhi is also included among the fifteen Koshthangas of body. In Sharirasthana of Sushruta Samhita; Acharya Sushruta mentioned that Sira and Dhamani are originated from Nabhi. Acharya Vagbhatta has quoted Nabhi as a dominant place of Pitta Dosha. Nabhi is an abode of Pranas (vital energy). Available literature and commentary on Nabhi interprets it as a Navel but practically it doesn’t make a sense to stick with this interpretation. Therefore; it is need to review classical texts of Ayurveda and contemporary literature to get clear and unambiguous meaning of the word “Nabhi” now a day. After thoroughly reading and interpreting the literature available regarding Nabhi; core of physiological process would be considered by the term Nabhi.

scholarly journals Effect of Ultrasound-Assisted Extraction Parameters on Total Polyphenols and Its Antioxidant Activity from Mango Residues (Mangifera indica L. var. Manililla)

Separations ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 94
Author(s):  
Anahí J. Borrás-Enríquez ◽  
Elizabeth Reyes-Ventura ◽  
Socorro J. Villanueva-Rodríguez ◽  
Lorena Moreno-Vilet
Keyword(s):  
Antioxidant Activity ◽  
Mangifera Indica ◽  
Central Point ◽  
Added Value ◽  
Sonication Time ◽  
Ultrasound Assisted Extraction ◽  
Extraction Technology ◽  
Total Polyphenols ◽  
Assisted Extraction ◽  
Ultrasound Assisted

Manililla is a mango variety whose residues contain bioactive compounds such as polyphenols and flavonoids, with high added value. The use of environmentally friendly extraction technology would be of great relevance; hence, this study aimed to evaluate the effect of solvent relation, sonication time and amplitude on the ultrasound-assisted extraction of total polyphenols in Manililla mango residues (peel, endocarp and kernel) and antioxidant activity. An experimental design 23 with a central point was used to evaluate the curvature behavior of the process variables. Conventional maceration was used as a control. The better conditions were obtained at the central point using 50% ethanol in water, 60% amplitude and 20 min of sonication time. We obtained values of up to 1814 mg GAE/100 g, 469 mg GAE/100 g and 672 mg GAE/100 g of total polyphenols and 1228 mg QE/100 g, 653 mg QE/100 g and 880 mg QE/100 g of total flavonoids for peel, endocarp and kernel, respectively. Mangiferin was quantified in ultrasound-assisted extraction at 150 mg/g in peel and 0.025 mg/g in the kernel, but it was not detectable in maceration. An antioxidant capacity of 87%, 14% and 83% inhibition for peel, endocarp and kernel, respectively, were obtained. Peel and kernel were the residues with higher potential as extraction material, while endocarp was not.

scholarly journals On the Bloch–Kato conjecture for Hilbert modular forms

2021 ◽  
Author(s):  
Matteo Tamiozzo
Keyword(s):  
Modular Forms ◽  
Automorphic Forms ◽  
Euler System ◽  
Central Point ◽  
Shimura Curves ◽  
Hilbert Modular Forms ◽  
Reciprocity Laws ◽  
Hilbert Modular ◽  
Special Points

AbstractThe aim of this paper is to prove inequalities towards instances of the Bloch–Kato conjecture for Hilbert modular forms of parallel weight two, when the order of vanishing of the L-function at the central point is zero or one. We achieve this implementing an inductive Euler system argument which relies on explicit reciprocity laws for cohomology classes constructed using congruences of automorphic forms and special points on several Shimura curves.

scholarly journals On some automorphic properties of Galois traces of class invariants from generalized Weber functions of level 5

2019 ◽  
Vol 17 (1) ◽  
pp. 1631-1651
Author(s):  
Ick Sun Eum ◽  
Ho Yun Jung
Keyword(s):  
Modular Forms ◽  
Fourier Coefficients ◽  
Singular Values ◽  
Congruence Subgroups ◽  
Maass Form ◽  
Weakly Holomorphic Modular Forms ◽  
Reciprocity Law ◽  
Class Invariants ◽  
Higher Genus ◽  
Holomorphic Modular Forms

Abstract After the significant work of Zagier on the traces of singular moduli, Jeon, Kang and Kim showed that the Galois traces of real-valued class invariants given in terms of the singular values of the classical Weber functions can be identified with the Fourier coefficients of weakly holomorphic modular forms of weight 3/2 on the congruence subgroups of higher genus by using the Bruinier-Funke modular traces. Extending their work, we construct real-valued class invariants by using the singular values of the generalized Weber functions of level 5 and prove that their Galois traces are Fourier coefficients of a harmonic weak Maass form of weight 3/2 by using Shimura’s reciprocity law.

scholarly journals A topological central point theorem

2012 ◽  
Vol 159 (3) ◽  
pp. 864-868 ◽  
Author(s):  
Roman N. Karasev
Keyword(s):  
Point Theorem ◽  
Central Point

Again on relative clause and subordination in Latin

2014 ◽  
Vol 13 (1) ◽  
Author(s):  
Gualtiero Calboli
Keyword(s):  
Relative Clause ◽  
Syntactic Structure ◽  
Central Point ◽  
Relative Pronoun ◽  
Case Theory ◽  
Nominative Case ◽  
Subordinate Clauses ◽  
Long Time ◽  
The Subject ◽  
The Law

AbstractI started from the relative clause which occurs in Hittite, and in particular with the enclitic position of the relative pronoun. This is connected with the OV position and this position seems to have been prevailing in Hittite and PIE. The syntactic structure usually employed in Hittite between different clauses is the parataxis. Nevertheless, also the hypotaxis begins to be employed and the best occasion to use it was the diptych as suggested by Haudry, though he didn't consider the most natural and usual diptych: the law, where the crime and the sanction build a natural diptych already in old Hittite. Then I used Justus' and Boley's discussion on the structure of Hittite sentence and found a similarity with Latin, namely the use of an animate subject as central point of a sentence. With verbs of action in ancient languages the subject was normally an animate being, whereas also inanimate subject is employed in modern languages. This seems to be the major difference between ancient and modern structure of a sentence, or, better to say, in Hittite and PIE the subject was an animate being and this persisted a long time, and remained as a tendency in Latin, while in following languages and in classical grammar the subject became a simple nominal “entity” to be predicated and precised with verb and other linguistic instruments. A glance has been cast also to pronouns and particles (sometimes linked together) as instruments of linking nominal variants of coordinate or subordinate clauses and to the development of demonstrative/deictic pronouns. Also in ancient case theory a prevailing position was assured to the nominative case, the case of the subject.

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