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- W3095359602 abstract "Abstract We prove an analogue of Kronecker’s second limit formula for a continuous family of “indefinite zeta functions”. Indefinite zeta functions were introduced in the author’s previous paper as Mellin transforms of indefinite theta functions, as defined by Zwegers. Our formula is valid in dimension $$g=2$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> at $$s=1$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> or $$s=0$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> . For a choice of parameters obeying a certain symmetry, an indefinite zeta function is a differenced ray class zeta function of a real quadratic field, and its special value at $$s=0$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> was conjectured by Stark to be a logarithm of an algebraic unit. Our formula also permits practical high-precision computation of Stark ray class invariants." @default.
- W3095359602 created "2020-11-09" @default.
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- W3095359602 date "2023-05-22" @default.
- W3095359602 modified "2023-10-14" @default.
- W3095359602 title "A Kronecker limit formula for indefinite zeta functions" @default.
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- W3095359602 doi "https://doi.org/10.1007/s40687-023-00384-0" @default.
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