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Pythagoras0 (토론 | 기여) |
Pythagoras0 (토론 | 기여) |
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| (같은 사용자의 중간 판 7개는 보이지 않습니다) | |||
| 1번째 줄: | 1번째 줄: | ||
==개요== | ==개요== | ||
| − | * [[실해석적 아이젠슈타인 급수]] | + | * [[실해석적 아이젠슈타인 급수]] <math>E(\tau,s)</math>에 대하여, 다음이 성립 |
:<math>E(\tau,s) = {\pi\over s-1} + 2\pi\left(\gamma-\log(2)-\log(\sqrt{y}|\eta(\tau)|^2)\right) +O(s-1)</math> | :<math>E(\tau,s) = {\pi\over s-1} + 2\pi\left(\gamma-\log(2)-\log(\sqrt{y}|\eta(\tau)|^2)\right) +O(s-1)</math> | ||
여기서 <math>\gamma</math> 는 [[오일러상수, 감마]], <math>\eta(\tau)</math>는 [[데데킨트 에타함수]] | 여기서 <math>\gamma</math> 는 [[오일러상수, 감마]], <math>\eta(\tau)</math>는 [[데데킨트 에타함수]] | ||
| 7번째 줄: | 7번째 줄: | ||
==메모== | ==메모== | ||
* http://www.ms.u-tokyo.ac.jp/~t-saito/pp/GR2.pdf | * http://www.ms.u-tokyo.ac.jp/~t-saito/pp/GR2.pdf | ||
| + | * [[Herglotz–Zagier 함수]] | ||
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| + | ==관련된 항목들== | ||
| + | * [[엡슈타인 제타함수]] | ||
| 14번째 줄: | 19번째 줄: | ||
==관련논문== | ==관련논문== | ||
| + | * Anna-Maria von Pippich, A Kronecker limit type formula for elliptic Eisenstein series, arXiv:1604.00811[math.NT], April 04 2016, http://arxiv.org/abs/1604.00811v1 | ||
| + | * Jorgenson, Jay, Anna-Maria von Pippich, and Lejla Smajlovic. ‘Applications of Kronecker’s Limit Formula for Elliptic Eisenstein Series’. arXiv:1505.02812 Null, 11 May 2015. http://arxiv.org/abs/1505.02812. | ||
| + | * Agashe, Amod. “A Generalization of Kronecker’s First Limit Formula.” arXiv:1501.00453 [math], January 2, 2015. http://arxiv.org/abs/1501.00453. | ||
* Ramachandra, K. 1964. “Some Applications of Kronecker’s Limit Formulas.” Annals of Mathematics 80 (1) (July 1): 104–148. doi:10.2307/1970494. | * Ramachandra, K. 1964. “Some Applications of Kronecker’s Limit Formulas.” Annals of Mathematics 80 (1) (July 1): 104–148. doi:10.2307/1970494. | ||
* http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=Kronecker%27s+limit+formulas | * http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=Kronecker%27s+limit+formulas | ||
| + | |||
| + | ==메타데이터== | ||
| + | ===위키데이터=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q3077651 Q3077651] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'LOWER': 'kronecker'}, {'LOWER': 'limit'}, {'LEMMA': 'formula'}] | ||
2021년 2월 17일 (수) 02:27 기준 최신판
개요
- 실해석적 아이젠슈타인 급수 \(E(\tau,s)\)에 대하여, 다음이 성립
\[E(\tau,s) = {\pi\over s-1} + 2\pi\left(\gamma-\log(2)-\log(\sqrt{y}|\eta(\tau)|^2)\right) +O(s-1)\] 여기서 \(\gamma\) 는 오일러상수, 감마, \(\eta(\tau)\)는 데데킨트 에타함수
메모
관련된 항목들
사전 형태의 자료
관련논문
- Anna-Maria von Pippich, A Kronecker limit type formula for elliptic Eisenstein series, arXiv:1604.00811[math.NT], April 04 2016, http://arxiv.org/abs/1604.00811v1
- Jorgenson, Jay, Anna-Maria von Pippich, and Lejla Smajlovic. ‘Applications of Kronecker’s Limit Formula for Elliptic Eisenstein Series’. arXiv:1505.02812 Null, 11 May 2015. http://arxiv.org/abs/1505.02812.
- Agashe, Amod. “A Generalization of Kronecker’s First Limit Formula.” arXiv:1501.00453 [math], January 2, 2015. http://arxiv.org/abs/1501.00453.
- Ramachandra, K. 1964. “Some Applications of Kronecker’s Limit Formulas.” Annals of Mathematics 80 (1) (July 1): 104–148. doi:10.2307/1970494.
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=Kronecker%27s+limit+formulas
메타데이터
위키데이터
- ID : Q3077651
Spacy 패턴 목록
- [{'LOWER': 'kronecker'}, {'LOWER': 'limit'}, {'LEMMA': 'formula'}]