On the proportion of quadratic character twists of L-functions attached to cusp forms not vanishing at the central point

1999 ◽  
Vol 1999 (508) ◽  
pp. 179-187 ◽  
Author(s):  
Winfried Kohnen
Keyword(s):  
Central Point ◽  
Cusp Forms ◽  
Quadratic Character

An Elementary Proof of a Weak Exceptional Zero Conjecture

2004 ◽  
Vol 56 (2) ◽  
pp. 373-405 ◽  
Author(s):  
Louisa Orton
Keyword(s):  
Elementary Proof ◽  
Central Point ◽  
Cusp Forms ◽  
Dirichlet Characters

AbstractIn this paper we extend Darmon's theory of “integration on ℋp × ℋ” to cusp forms f of higher even weight. This enables us to prove a “weak exceptional zero conjecture”: that when the p-adic L-function of f has an exceptional zero at the central point, the ℒ-invariant arising is independent of a twist by certain Dirichlet characters.

scholarly journals MOMENTS AND HYBRID SUBCONVEXITY FOR SYMMETRIC-SQUARE L-FUNCTIONS

2021 ◽  
pp. 1-45
Author(s):  
RIZWANUR KHAN ◽  
MATTHEW P. YOUNG
Keyword(s):  
Spectral Parameter ◽  
Critical Line ◽  
Short Interval ◽  
Central Point ◽  
Cusp Forms ◽  
Sharp Bounds ◽  
Second Moment ◽  
Symmetric Square

Abstract We establish sharp bounds for the second moment of symmetric-square L-functions attached to Hecke Maass cusp forms $u_j$ with spectral parameter $t_j$ , where the second moment is a sum over $t_j$ in a short interval. At the central point $s=1/2$ of the L-function, our interval is smaller than previous known results. More specifically, for $\left \lvert t_j\right \rvert $ of size T, our interval is of size $T^{1/5}$ , whereas the previous best was $T^{1/3}$ , from work of Lam. A little higher up on the critical line, our second moment yields a subconvexity bound for the symmetric-square L-function. More specifically, we get subconvexity at $s=1/2+it$ provided $\left \lvert t_j\right \rvert ^{6/7+\delta }\le \lvert t\rvert \le (2-\delta )\left \lvert t_j\right \rvert $ for any fixed $\delta>0$ . Since $\lvert t\rvert $ can be taken significantly smaller than $\left \lvert t_j\right \rvert $ , this may be viewed as an approximation to the notorious subconvexity problem for the symmetric-square L-function in the spectral aspect at $s=1/2$ .

Congruences between Hilbert Cusp Forms

2018 ◽  
Author(s):  
Hiroshi Saito ◽  
Masatoshi Yamauchi
Keyword(s):  
Cusp Forms

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.

Construction of Binary Sequences With Low Correlation via Multiplicative Quadratic Character Over Finite Fields of Odd Characteristics

2021 ◽  
Vol 67 (4) ◽  
pp. 2236-2244
Author(s):  
Lingfei Jin ◽  
Dawei Chen ◽  
Luyan Qian ◽  
Jiaming Teng ◽  
Shijun Chen
Keyword(s):  
Finite Fields ◽  
Binary Sequences ◽  
Quadratic Character ◽  
Low Correlation

scholarly journals On triple correlations of Fourier coefficients of cusp forms

2018 ◽  
Vol 183 ◽  
pp. 485-492 ◽  
Author(s):  
Guangshi Lü ◽  
Ping Xi
Keyword(s):  
Fourier Coefficients ◽  
Cusp Forms

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.

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