Results 21 to 30 of about 508 (172)
Matching the (DR4)-R-6 interaction at two-loops [PDF]
, 2014 40 pages, various typos and coefficients corrected in version 2International audienceThe coefficient of the $D^6 {\cal R}^4$ interaction in the low energy expansion of the two-loop four-graviton amplitude in type II superstring theory is known to be ...
Pioline, Boris +13 more
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Automorphic Forms: New Directions [PDF]
, 2011 The workshop on Automorphic Forms: New Directions provided a nice glimpse of the many streams of current research activity in this very active area. Topics included the relative trace formula and periods of automorphic forms, Arthur packets and locally ...
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Lefschetz decompositions of Kudla–Millson theta functions
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract In the 1980s Kudla and Millson introduced a theta function in two variables. It behaves as a Siegel modular form with respect to the first variable, and is a closed differential form on an orthogonal Shimura variety X$X$ with respect to the other variable. We prove that the Lefschetz decomposition of the cohomology class of that theta function
Jan Hendrik Bruinier, Riccardo Zuffetti
wiley +1 more source
On the Lang–Trotter conjecture for Siegel modular forms
Mathematika, Volume 72, Issue 3, July 2026.Abstract Let f$f$ be a genus‐two cuspidal Siegel eigenform. We prove an adelic open image theorem for the compatible system of Galois representations associated with f$f$, generalizing the results of Ribet and Momose for elliptic modular forms. Using this result, we investigate the distribution of the Hecke eigenvalues ap$a_p$ of f$f$, and obtain upper
Arvind Kumar, Moni Kumari, Ariel Weiss
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Primitivity testing in free group algebras via duality
Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.Abstract Let K$K$ be a field and F$F$ a free group. By a classical result of Cohn and Lewin, the free group algebra KF$K\left[F\right]$ is a free ideal ring (FIR): a ring over which the submodules of free modules are themselves free, and of a well‐defined rank. Given a finitely generated right ideal I⩽KF$I\leqslant K\left[F\right]$ and an element f∈I$f\
Matan Seidel +2 more
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Algebraicity of ratios of special L$L$‐values for GL(n)$\mathrm{GL}(n)$
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract We prove, under certain assumptions, the algebraicity of the ratio L(m,Π×χ)/L(m,Π×χ′)$L(m, \Pi \times \chi)/L(m, \Pi \times \chi ^{\prime })$, where Π$\Pi$ is a cuspidal automorphic cohomological unitary representation of GLn(AQ)$\mathrm{GL}_n(\mathbb {A}_\mathbb {Q})$, and χ$\chi$, χ′$\chi ^{\prime }$ are finite‐order Hecke characters such ...
Ankit Rai, Gunja Sachdeva
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Conference L-Functions and Automorphic Forms
, 2017 This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016.
Bruinier, Jan, Kohnen, Winfried
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Fortschritte der Physik, Volume 74, Issue 4, April 2026.Abstract String theory has strong implications for cosmology, implying the absence of a cosmological constant, ruling out single‐field slow‐roll inflation, and that black holes decay. The origins of these statements are elucidated within the string‐theoretical swampland programme.
Kay Lehnert
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CM values of higher automorphic Green functions for orthogonal groups
, 2021 Gross and Zagier conjectured that the CM values (of certain Hecke translates) of the automorphic Green function Gs (z₁, z₂) for the elliptic modular group at positive integral spectral parameter s are given by logarithms of algebraic numbers in suitable ...
Bruinier, Jan Hendrik +2 more
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Distribution of integer points on determinant surfaces and a mod‐p analogue
Mathematika, Volume 72, Issue 2, April 2026.Abstract We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form xy−zw=r$xy-zw=r$, where r$r$ is a non‐zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables x,y,z,w$x, y, z, w$ as well as of r$r$.
Satadal Ganguly, Rachita Guria
wiley +1 more source