Results 41 to 50 of about 3,429,146 (271)
Congruences with Eisenstein series and -invariants [PDF]
Compositio Mathematica, 2019 We study the variation of$\unicode[STIX]{x1D707}$-invariants in Hida families with residually reducible Galois representations. We prove a lower bound for these invariants which is often expressible in terms of the$p$-adic zeta function. This lower bound forces these$\unicode[STIX]{x1D707}$-invariants to be unbounded along the family, and we conjecture
Bellaïche, Joël, Pollack, Robert
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Relation between Borweins’ Cubic Theta Functions and Ramanujan’s Eisenstein Series
Journal of Applied Mathematics, 2021 Two-dimensional theta functions were found by the Borwein brothers to work on Gauss and Legendre’s arithmetic-geometric mean iteration. In this paper, some new Eisenstein series identities are obtained by using (p, k)-parametrization in terms of Borweins’
B. R. Srivatsa Kumar +2 more
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Algorithms and tools for iterated Eisenstein integrals
Journal of High Energy Physics, 2020 We present algorithms to work with iterated Eisenstein integrals that have recently appeared in the computation of multi-loop Feynman integrals. These algorithms allow one to analytically continue these integrals to all regions of the parameter space ...
Claude Duhr, Lorenzo Tancredi
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A p-adic Eisenstein measure for vector-weight automorphic forms [PDF]
, 2014 We construct a p-adic Eisenstein measure with values in the space of vector-weight p-adic automorphic forms on certain unitary groups. This measure allows us to p-adically interpolate special values of certain vector-weight C-infinity automorphic forms ...
Eischen, Ellen
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Eisenstein series for infinite-dimensional U-duality groups [PDF]
, 2012 We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes.
A Basu +74 more
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Effective Lower Bounds for L(1,{\chi}) via Eisenstein Series [PDF]
, 2016 We give effective lower bounds for $L(1,\chi)$ via Eisenstein series on $\Gamma_0(q) \backslash \mathbb{H}$. The proof uses the Maass-Selberg relation for truncated Eisenstein series and sieve theory in the form of the Brun-Titchmarsh inequality.
Humphries, Peter
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Eisenstein series and convolution sums [PDF]
The Ramanujan Journal, 2018 We compute Fourier series expansions of weight $2$ and weight $4$ Eisenstein series at various cusps. Then we use results of these computations to give formulas for the convolution sums $ \sum_{a+p b=n} (a) (b)$, $ \sum_{p_1a+p_2 b=n} (a) (b)$ and $ \sum_{a+p_1 p_2 b=n} (a) (b)$ where $p, p_1, p_2$ are primes.
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One-loop open-string integrals from differential equations: all-order α′-expansions at n points
Journal of High Energy Physics, 2020 We study generating functions of moduli-space integrals at genus one that are expected to form a basis for massless n-point one-loop amplitudes of open superstrings and open bosonic strings.
Carlos R. Mafra, Oliver Schlotterer
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Quantum Variance for Eisenstein Series [PDF]
International Mathematics Research Notices, 2019 Abstract In this paper, we prove an asymptotic formula for the quantum variance for Eisenstein series on $\operatorname{PSL}_2(\mathbb{Z})\backslash \mathbb{H}$. The resulting quadratic form is compared with the classical variance and the quantum variance for cusp forms.
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