크로네커 극한 공식

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

• http://www.ms.u-tokyo.ac.jp/~t-saito/pp/GR2.pdf
• Herglotz–Zagier 함수

관련된 항목들

• 엡슈타인 제타함수

사전 형태의 자료

• http://en.wikipedia.org/wiki/Kronecker_limit_formula

관련논문

• 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